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Type | Label | Description |
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Statement | ||
Theorem | ee101 37101 | e101 37100 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e011 37102 | A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee011 37103 | e011 37102 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e100 37104 | A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee100 37105 | e100 37104 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e010 37106 | A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee010 37107 | e010 37106 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e001 37108 | A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee001 37109 | e001 37108 without virtual deductions. (Contributed by Alan Sare, 23-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e11 37110 | A virtual deduction elimination rule. (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e11an 37111 | Conjunction form of e11 37110. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee11an 37112 | e11an 37111 without virtual deductions. syl22anc 1277 is also e11an 37111 without virtual deductions, exept with a different order of hypotheses. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e01 37113 | A virtual deduction elimination rule. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e01an 37114 | Conjunction form of e01 37113. (Contributed by Alan Sare, 11-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee01an 37115 | e01an 37114 without virtual deductions. sylancr 674 is also a form of e01an 37114 without virtual deduction, except the order of the hypotheses is different. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e10 37116 | A virtual deduction elimination rule (see mpisyl 21). (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e10an 37117 | Conjunction form of e10 37116. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee10an 37118 | e10an 37117 without virtual deductions. sylancl 673 is also e10an 37117 without virtual deductions, except the order of the hypotheses is different. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e02 37119 | A virtual deduction elimination rule. (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e02an 37120 | Conjunction form of e02 37119. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee02an 37121 | e02an 37120 without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | eel021old 37122 | el021old 37123 without virtual deductions. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | el021old 37123 | A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | eel132 37124 | syl2an 484 with antecedents in standard conjunction form. (Contributed by Alan Sare, 26-Aug-2016.) |
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Theorem | eel2221 37125 | Deduction related to syl3an 1318 with antecedents in standard conjunction form. (Contributed by Alan Sare, 31-Aug-2016.) |
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Theorem | eel000cT 37126 | An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | eel0TT 37127 | An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | eelT00 37128 | An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | eelTTT 37129 | An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | eelT11 37130 | An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | eel012 37131 | mp3an 1373 with antecedents in standard conjunction form and with two hypotheses which are implications. (Contributed by Alan Sare, 28-Aug-2016.) |
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Theorem | eel0121 37132 | An elimination deduction. (Contributed by Alan Sare, 17-Oct-2017.) |
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Theorem | eelT1 37133 | Syllogism inference combined with modus ponens. (Contributed by Jeff Madsen, 2-Sep-2009.) (Revised by Alan Sare, 23-Dec-2016.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | eelT12 37134 | An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | eelTT1 37135 | An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | eelT01 37136 | An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | eel0T1 37137 | An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | eel12131 37138 | An elimination deduction. (Contributed by Alan Sare, 17-Oct-2017.) |
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Theorem | eel2131 37139 | syl2an 484 with antecedents in standard conjunction form. (Contributed by Alan Sare, 26-Aug-2016.) |
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Theorem | eel3132 37140 | syl2an 484 with antecedents in standard conjunction form. (Contributed by Alan Sare, 27-Aug-2016.) |
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Theorem | eel0321old 37141 | el0321old 37142 without virtual deductions. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | el0321old 37142 | A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | eel2122old 37143 | el2122old 37144 without virtual deductions. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | el2122old 37144 | A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | eel0001 37145 | An elimination deduction. (Contributed by Alan Sare, 17-Oct-2017.) |
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Theorem | eel0000 37146 | Elimination rule similar to mp4an 684, except with a left-nested conjunction unification theorem. (Contributed by Alan Sare, 17-Oct-2017.) |
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Theorem | eel1111 37147 | Four-hypothesis elimination deduction for an assertion with a singleton virtual hypothesis collection. Similar to syl112anc 1280 except the unification theorem uses left-nested conjunction. (Contributed by Alan Sare, 17-Oct-2017.) |
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Theorem | eel00001 37148 | An elimination deduction. (Contributed by Alan Sare, 17-Oct-2017.) |
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Theorem | eel00000 37149 | Elimination rule similar eel0000 37146, except with five hpothesis steps. (Contributed by Alan Sare, 17-Oct-2017.) |
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Theorem | eel11111 37150 | Five-hypothesis elimination deduction for an assertion with a singleton virtual hypothesis collection. Similar to syl113anc 1288 except the unification theorem uses left-nested conjunction. (Contributed by Alan Sare, 17-Oct-2017.) |
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Theorem | e12 37151 | A virtual deduction elimination rule (see sylsyld 58). (Contributed by Alan Sare, 21-Apr-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e12an 37152 | Conjunction form of e12 37151 (see syl6an 552). (Contributed by Alan Sare, 11-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | el12 37153 | Virtual deduction form of syl2an 484. (Contributed by Alan Sare, 23-Apr-2015.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e20 37154 | A virtual deduction elimination rule (see syl6mpi 64). (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e20an 37155 | Conjunction form of e20 37154. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee20an 37156 | e20an 37155 without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e21 37157 | A virtual deduction elimination rule (see syl6ci 67). (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e21an 37158 | Conjunction form of e21 37157. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee21an 37159 | e21an 37158 without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e333 37160 | A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e33 37161 | A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e33an 37162 | Conjunction form of e33 37161. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee33an 37163 | e33an 37162 without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e3 37164 | Meta-connective form of syl8 72. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e3bi 37165 | Biconditional form of e3 37164. syl8ib 239 is e3bi 37165 without virtual deductions. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e3bir 37166 | Right biconditional form of e3 37164. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e03 37167 | A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee03 37168 | e03 37167 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e03an 37169 | Conjunction form of e03 37167. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee03an 37170 | Conjunction form of ee03 37168. (Contributed by Alan Sare, 18-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e30 37171 | A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee30 37172 | e30 37171 without virtual deductions. (Contributed by Alan Sare, 17-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e30an 37173 | A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee30an 37174 | Conjunction form of ee30 37172. (Contributed by Alan Sare, 17-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e13 37175 | A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e13an 37176 | A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee13an 37177 | e13an 37176 without virtual deductions. (Contributed by Alan Sare, 8-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e31 37178 | A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee31 37179 | e31 37178 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e31an 37180 | A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee31an 37181 | e31an 37180 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e23 37182 | A virtual deduction elimination rule (see syl10 75). (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e23an 37183 | A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee23an 37184 | e23an 37183 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e32 37185 | A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee32 37186 | e32 37185 without virtual deductions. (Contributed by Alan Sare, 18-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e32an 37187 | A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee32an 37188 | e33an 37162 without virtual deductions. (Contributed by Alan Sare, 14-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e123 37189 | A virtual deduction elimination rule. (Contributed by Alan Sare, 12-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | ee123 37190 | e123 37189 without virtual deductions. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | el123 37191 | A virtual deduction elimination rule. (Contributed by Alan Sare, 13-Jun-2015.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e233 37192 | A virtual deduction elimination rule. (Contributed by Alan Sare, 29-Feb-2012.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e323 37193 | A virtual deduction elimination rule. (Contributed by Alan Sare, 17-Apr-2012.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e000 37194 | A virtual deduction elimination rule. The non-virtual deduction form of e000 37194 is the virtual deduction form. (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e00 37195 | Elimination rule identical to mp2 9. The non-virtual deduction form is the virtual deduction form, which is mp2 9. (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e00an 37196 | Elimination rule identical to mp2an 683. The non-virtual deduction form is the virtual deduction form, which is mp2an 683. (Contributed by Alan Sare, 15-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | eel00cT 37197 | An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | eelTT 37198 | An elimination deduction. (Contributed by Alan Sare, 4-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | e0a 37199 | Elimination rule identical to ax-mp 5. The non-virtual deduction form is the virtual deduction form, which is ax-mp 5. (Contributed by Alan Sare, 14-Jun-2011.) (Proof modification is discouraged.) (New usage is discouraged.) |
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Theorem | eelT 37200 | An elimination deduction. (Contributed by Alan Sare, 5-Feb-2017.) (Proof modification is discouraged.) (New usage is discouraged.) |
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