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Theorem f1eq3 5032
Description: Equality theorem for one-to-one functions. (Contributed by NM, 10-Feb-1997.)
Assertion
Ref Expression
f1eq3  F : C -1-1->  F : C -1-1->

Proof of Theorem f1eq3
StepHypRef Expression
1 feq3 4975 . . 3  F : C -->  F : C
-->
21anbi1d 438 . 2  F : C -->  Fun  `' F  F : C -->  Fun  `' F
3 df-f1 4850 . 2  F : C -1-1->  F : C -->  Fun  `' F
4 df-f1 4850 . 2  F : C -1-1->  F : C -->  Fun  `' F
52, 3, 43bitr4g 212 1  F : C -1-1->  F : C -1-1->
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   wceq 1242   `'ccnv 4287   Fun wfun 4839   -->wf 4841   -1-1->wf1 4842
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-in 2918  df-ss 2925  df-f 4849  df-f1 4850
This theorem is referenced by:  f1oeq3  5062  f1eq123d  5064  tposf12  5825  brdomg  6165
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