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Mirrors > Home > ILE Home > Th. List > opelopab | Unicode version |
Description: The law of concretion. Theorem 9.5 of [Quine] p. 61. (Contributed by NM, 16-May-1995.) |
Ref | Expression |
---|---|
opelopab.1 | |
opelopab.2 | |
opelopab.3 | |
opelopab.4 |
Ref | Expression |
---|---|
opelopab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opelopab.1 | . 2 | |
2 | opelopab.2 | . 2 | |
3 | opelopab.3 | . . 3 | |
4 | opelopab.4 | . . 3 | |
5 | 3, 4 | opelopabg 4241 | . 2 |
6 | 1, 2, 5 | mp2an 423 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1342 wcel 2135 cvv 2722 cop 3574 copab 4037 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-14 2138 ax-ext 2146 ax-sep 4095 ax-pow 4148 ax-pr 4182 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-eu 2016 df-mo 2017 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2724 df-un 3116 df-in 3118 df-ss 3125 df-pw 3556 df-sn 3577 df-pr 3578 df-op 3580 df-opab 4039 |
This theorem is referenced by: opabid2 4730 dfres2 4931 xporderlem 6191 acfun 7155 ccfunen 7197 |
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