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Mirrors > Home > ILE Home > Th. List > class2seteq | Unicode version |
Description: Equality theorem for classes and sets . (Contributed by NM, 13-Dec-2005.) (Proof shortened by Raph Levien, 30-Jun-2006.) |
Ref | Expression |
---|---|
class2seteq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex 2610 | . 2 | |
2 | ax-1 5 | . . . . 5 | |
3 | 2 | ralrimiv 2433 | . . . 4 |
4 | rabid2 2530 | . . . 4 | |
5 | 3, 4 | sylibr 132 | . . 3 |
6 | 5 | eqcomd 2086 | . 2 |
7 | 1, 6 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1284 wcel 1433 wral 2348 crab 2352 cvv 2601 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-ral 2353 df-rab 2357 df-v 2603 |
This theorem is referenced by: (None) |
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