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Mirrors > Home > ILE Home > Th. List > isoeq3 | Unicode version |
Description: Equality theorem for isomorphisms. (Contributed by NM, 17-May-2004.) |
Ref | Expression |
---|---|
isoeq3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq 3989 | . . . . 5 | |
2 | 1 | bibi2d 231 | . . . 4 |
3 | 2 | 2ralbidv 2494 | . . 3 |
4 | 3 | anbi2d 461 | . 2 |
5 | df-isom 5205 | . 2 | |
6 | df-isom 5205 | . 2 | |
7 | 4, 5, 6 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 wral 2448 class class class wbr 3987 wf1o 5195 cfv 5196 wiso 5197 |
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 1440 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-4 1503 ax-17 1519 ax-ial 1527 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-cleq 2163 df-clel 2166 df-ral 2453 df-br 3988 df-isom 5205 |
This theorem is referenced by: (None) |
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