Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 5371 | . . 3 | |
2 | foeq2 5389 | . . 3 | |
3 | 1, 2 | anbi12d 465 | . 2 |
4 | df-f1o 5177 | . 2 | |
5 | df-f1o 5177 | . 2 | |
6 | 3, 4, 5 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1335 wf1 5167 wfo 5168 wf1o 5169 |
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 1427 ax-gen 1429 ax-4 1490 ax-17 1506 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-cleq 2150 df-fn 5173 df-f 5174 df-f1 5175 df-fo 5176 df-f1o 5177 |
This theorem is referenced by: f1oeq23 5406 f1oeq123d 5409 f1oeq2d 5410 f1osng 5455 isoeq4 5754 bren 6692 f1dmvrnfibi 6888 summodclem3 11277 summodclem2a 11278 summodc 11280 fsum3 11284 fsumf1o 11287 sumsnf 11306 fprodf1o 11485 prodsnf 11489 |
Copyright terms: Public domain | W3C validator |