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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 2049 | . . 3 | |
2 | 1 | 3anbi2d 1212 | . 2 |
3 | df-er 6106 | . 2 | |
4 | df-er 6106 | . 2 | |
5 | 2, 3, 4 | 3bitr4g 212 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 w3a 885 wceq 1243 cun 2915 wss 2917 ccnv 4344 cdm 4345 ccom 4349 wrel 4350 wer 6103 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-5 1336 ax-gen 1338 ax-4 1400 ax-17 1419 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-cleq 2033 df-er 6106 |
This theorem is referenced by: iserd 6132 |
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