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Mirrors > Home > ILE Home > Th. List > ereq2 | Unicode version |
Description: Equality theorem for equivalence predicate. (Contributed by Mario Carneiro, 12-Aug-2015.) |
Ref | Expression |
---|---|
ereq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq2 2174 | . . 3 | |
2 | 1 | 3anbi2d 1306 | . 2 |
3 | df-er 6495 | . 2 | |
4 | df-er 6495 | . 2 | |
5 | 2, 3, 4 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 w3a 967 wceq 1342 cun 3112 wss 3114 ccnv 4600 cdm 4601 ccom 4605 wrel 4606 wer 6492 |
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-5 1434 ax-gen 1436 ax-4 1497 ax-17 1513 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-cleq 2157 df-er 6495 |
This theorem is referenced by: iserd 6521 |
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