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Theorem foeq3 5047
Description: Equality theorem for onto functions. (Contributed by NM, 1-Aug-1994.)
Assertion
Ref Expression
foeq3  F : C -onto->  F : C -onto->

Proof of Theorem foeq3
StepHypRef Expression
1 eqeq2 2046 . . 3  ran  F  ran  F
21anbi2d 437 . 2  F  Fn  C  ran  F  F  Fn  C  ran  F
3 df-fo 4851 . 2  F : C -onto->  F  Fn  C  ran  F
4 df-fo 4851 . 2  F : C -onto->  F  Fn  C  ran  F
52, 3, 43bitr4g 212 1  F : C -onto->  F : C -onto->
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98   wceq 1242   ran crn 4289    Fn wfn 4840   -onto->wfo 4843
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-gen 1335  ax-4 1397  ax-17 1416  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-fo 4851
This theorem is referenced by:  f1oeq3  5062  foeq123d  5065  resdif  5091  ffoss  5101
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