Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > f1eq3 | Unicode version |
Description: Equality theorem for one-to-one functions. (Contributed by NM, 10-Feb-1997.) |
Ref | Expression |
---|---|
f1eq3 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | feq3 5252 | . . 3 | |
2 | 1 | anbi1d 460 | . 2 |
3 | df-f1 5123 | . 2 | |
4 | df-f1 5123 | . 2 | |
5 | 2, 3, 4 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 ccnv 4533 wfun 5112 wf 5114 wf1 5115 |
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-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-in 3072 df-ss 3079 df-f 5122 df-f1 5123 |
This theorem is referenced by: f1oeq3 5353 f1eq123d 5355 tposf12 6159 brdomg 6635 |
Copyright terms: Public domain | W3C validator |