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Mirrors > Home > ILE Home > Th. List > f1oeq2 | Unicode version |
Description: Equality theorem for one-to-one onto functions. (Contributed by NM, 10-Feb-1997.) |
Ref | Expression |
---|---|
f1oeq2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | f1eq2 5324 | . . 3 | |
2 | foeq2 5342 | . . 3 | |
3 | 1, 2 | anbi12d 464 | . 2 |
4 | df-f1o 5130 | . 2 | |
5 | df-f1o 5130 | . 2 | |
6 | 3, 4, 5 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wf1 5120 wfo 5121 wf1o 5122 |
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-4 1487 ax-17 1506 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-cleq 2132 df-fn 5126 df-f 5127 df-f1 5128 df-fo 5129 df-f1o 5130 |
This theorem is referenced by: f1oeq23 5359 f1oeq123d 5362 f1oeq2d 5363 f1osng 5408 isoeq4 5705 bren 6641 f1dmvrnfibi 6832 summodclem3 11149 summodclem2a 11150 summodc 11152 fsum3 11156 fsumf1o 11159 sumsnf 11178 |
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