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Mirrors > Home > ILE Home > Th. List > breq | Unicode version |
Description: Equality theorem for binary relations. (Contributed by NM, 4-Jun-1995.) |
Ref | Expression |
---|---|
breq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq2 2101 | . 2 | |
2 | df-br 3765 | . 2 | |
3 | df-br 3765 | . 2 | |
4 | 1, 2, 3 | 3bitr4g 212 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 98 wceq 1243 wcel 1393 cop 3378 class class class wbr 3764 |
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-ie1 1382 ax-ie2 1383 ax-4 1400 ax-17 1419 ax-ial 1427 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-cleq 2033 df-clel 2036 df-br 3765 |
This theorem is referenced by: breqi 3770 breqd 3775 poeq1 4036 soeq1 4052 frforeq1 4080 weeq1 4093 fveq1 5177 foeqcnvco 5430 f1eqcocnv 5431 isoeq2 5442 isoeq3 5443 ofreq 5715 shftfvalg 9419 shftfval 9422 |
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