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Mathbox for Jonathan Ben-Naim |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > bnj1177 | Structured version Visualization version Unicode version |
Description: Technical lemma for bnj69 29812. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bnj1177.2 |
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bnj1177.3 |
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bnj1177.9 |
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bnj1177.13 |
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bnj1177.17 |
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Ref | Expression |
---|---|
bnj1177 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj1177.9 |
. . 3
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2 | df-bnj15 29491 |
. . . 4
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3 | 2 | simplbi 462 |
. . 3
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4 | 1, 3 | syl 17 |
. 2
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5 | bnj1177.3 |
. . . 4
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6 | bnj1147 29796 |
. . . . 5
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7 | ssinss1 3659 |
. . . . 5
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8 | 6, 7 | ax-mp 5 |
. . . 4
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9 | 5, 8 | eqsstri 3461 |
. . 3
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10 | 9 | a1i 11 |
. 2
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11 | bnj1177.17 |
. . . . . . 7
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12 | bnj906 29734 |
. . . . . . 7
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13 | 1, 11, 12 | syl2anc 666 |
. . . . . 6
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14 | ssrin 3656 |
. . . . . 6
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15 | 13, 14 | syl 17 |
. . . . 5
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16 | bnj1177.13 |
. . . . . . . 8
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17 | bnj1177.2 |
. . . . . . . . . 10
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18 | 17 | simp2bi 1023 |
. . . . . . . . 9
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19 | 18 | adantl 468 |
. . . . . . . 8
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20 | 16, 19 | sseldd 3432 |
. . . . . . 7
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21 | 17 | simp3bi 1024 |
. . . . . . . 8
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22 | 21 | adantl 468 |
. . . . . . 7
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23 | bnj1152 29800 |
. . . . . . 7
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24 | 20, 22, 23 | sylanbrc 669 |
. . . . . 6
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25 | 24, 19 | elind 3617 |
. . . . 5
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26 | 15, 25 | sseldd 3432 |
. . . 4
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27 | ne0i 3736 |
. . . 4
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28 | 26, 27 | syl 17 |
. . 3
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29 | 5 | neeq1i 2687 |
. . 3
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30 | 28, 29 | sylibr 216 |
. 2
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31 | bnj893 29732 |
. . . 4
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32 | 1, 11, 31 | syl2anc 666 |
. . 3
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33 | inex1g 4545 |
. . . 4
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34 | 5, 33 | syl5eqel 2532 |
. . 3
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35 | 32, 34 | syl 17 |
. 2
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36 | 4, 10, 30, 35 | bnj951 29580 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-8 1888 ax-9 1895 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 ax-rep 4514 ax-sep 4524 ax-nul 4533 ax-pow 4580 ax-pr 4638 ax-un 6580 ax-reg 8104 ax-inf2 8143 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3or 985 df-3an 986 df-tru 1446 df-fal 1449 df-ex 1663 df-nf 1667 df-sb 1797 df-eu 2302 df-mo 2303 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2580 df-ne 2623 df-ral 2741 df-rex 2742 df-reu 2743 df-rab 2745 df-v 3046 df-sbc 3267 df-csb 3363 df-dif 3406 df-un 3408 df-in 3410 df-ss 3417 df-pss 3419 df-nul 3731 df-if 3881 df-pw 3952 df-sn 3968 df-pr 3970 df-tp 3972 df-op 3974 df-uni 4198 df-iun 4279 df-br 4402 df-opab 4461 df-mpt 4462 df-tr 4497 df-eprel 4744 df-id 4748 df-po 4754 df-so 4755 df-fr 4792 df-we 4794 df-xp 4839 df-rel 4840 df-cnv 4841 df-co 4842 df-dm 4843 df-rn 4844 df-res 4845 df-ima 4846 df-ord 5425 df-on 5426 df-lim 5427 df-suc 5428 df-iota 5545 df-fun 5583 df-fn 5584 df-f 5585 df-f1 5586 df-fo 5587 df-f1o 5588 df-fv 5589 df-om 6690 df-1o 7179 df-bnj17 29485 df-bnj14 29487 df-bnj13 29489 df-bnj15 29491 df-bnj18 29493 |
This theorem is referenced by: bnj1190 29810 |
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