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Mirrors > Home > MPE Home > Th. List > pleval2 | Structured version Visualization version Unicode version |
Description: Less-than-or-equal in terms of less-than. (sspss 3531 analog.) (Contributed by NM, 17-Oct-2011.) (Revised by Mario Carneiro, 8-Feb-2015.) |
Ref | Expression |
---|---|
pleval2.b |
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pleval2.l |
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pleval2.s |
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Ref | Expression |
---|---|
pleval2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pleval2.b |
. . . 4
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2 | pleval2.l |
. . . 4
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3 | pleval2.s |
. . . 4
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4 | 1, 2, 3 | pleval2i 16203 |
. . 3
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5 | 4 | 3adant1 1025 |
. 2
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6 | 2, 3 | pltle 16200 |
. . 3
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7 | 1, 2 | posref 16189 |
. . . . 5
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8 | 7 | 3adant3 1027 |
. . . 4
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9 | breq2 4405 |
. . . 4
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10 | 8, 9 | syl5ibcom 224 |
. . 3
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11 | 6, 10 | jaod 382 |
. 2
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12 | 5, 11 | impbid 194 |
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-sep 4524 ax-nul 4533 ax-pow 4580 ax-pr 4638 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 986 df-tru 1446 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-rab 2745 df-v 3046 df-sbc 3267 df-dif 3406 df-un 3408 df-in 3410 df-ss 3417 df-nul 3731 df-if 3881 df-sn 3968 df-pr 3970 df-op 3974 df-uni 4198 df-br 4402 df-opab 4461 df-mpt 4462 df-id 4748 df-xp 4839 df-rel 4840 df-cnv 4841 df-co 4842 df-dm 4843 df-iota 5545 df-fun 5583 df-fv 5589 df-preset 16166 df-poset 16184 df-plt 16197 |
This theorem is referenced by: pltletr 16210 plelttr 16211 tosso 16275 tlt3 28419 orngsqr 28560 |
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