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Mirrors > Home > ILE Home > Th. List > breqdi | Unicode version |
Description: Equality deduction for a binary relation. (Contributed by Thierry Arnoux, 5-Oct-2020.) |
Ref | Expression |
---|---|
breq1d.1 | |
breqdi.1 |
Ref | Expression |
---|---|
breqdi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breqdi.1 | . 2 | |
2 | breq1d.1 | . . 3 | |
3 | 2 | breqd 3940 | . 2 |
4 | 1, 3 | mpbid 146 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wceq 1331 class class class wbr 3929 |
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 2121 |
This theorem depends on definitions: df-bi 116 df-cleq 2132 df-clel 2135 df-br 3930 |
This theorem is referenced by: dvef 12856 |
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