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Mirrors > Home > MPE Home > Th. List > opabid | Structured version Visualization version Unicode version |
Description: The law of concretion. Special case of Theorem 9.5 of [Quine] p. 61. (Contributed by NM, 14-Apr-1995.) (Proof shortened by Andrew Salmon, 25-Jul-2011.) |
Ref | Expression |
---|---|
opabid |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opex 4663 |
. 2
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2 | copsexg 4686 |
. . 3
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3 | 2 | bicomd 205 |
. 2
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4 | df-opab 4461 |
. 2
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5 | 1, 3, 4 | elab2 3187 |
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-9 1895 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 ax-sep 4524 ax-nul 4533 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-rab 2745 df-v 3046 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-opab 4461 |
This theorem is referenced by: opelopabsb 4710 ssopab2b 4727 dmopab 5044 rnopab 5078 funopab 5614 opabiota 5926 fvopab5 5972 f1ompt 6042 ovid 6410 zfrep6 6758 enssdom 7591 omxpenlem 7670 infxpenlem 8441 canthwelem 9072 pospo 16212 2ndcdisj 20464 lgsquadlem1 24275 lgsquadlem2 24276 h2hlm 26626 opabdm 28212 opabrn 28213 fpwrelmap 28311 eulerpartlemgvv 29202 phpreu 31922 poimirlem26 31959 diclspsn 34756 areaquad 36095 |
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