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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 2201 | . 2 | |
2 | df-br 3925 | . 2 | |
3 | df-br 3925 | . 2 | |
4 | 1, 2, 3 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1331 wcel 1480 cop 3525 class class class wbr 3924 |
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 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-4 1487 ax-17 1506 ax-ial 1514 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-cleq 2130 df-clel 2133 df-br 3925 |
This theorem is referenced by: breqi 3930 breqd 3935 poeq1 4216 soeq1 4232 frforeq1 4260 weeq1 4273 fveq1 5413 foeqcnvco 5684 f1eqcocnv 5685 isoeq2 5696 isoeq3 5697 ofreq 5978 supeq3 6870 shftfvalg 10583 shftfval 10586 |
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