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Theorem foeq2 5046
Description: Equality theorem for onto functions. (Contributed by NM, 1-Aug-1994.)
Assertion
Ref Expression
foeq2  F : -onto-> C  F : -onto-> C

Proof of Theorem foeq2
StepHypRef Expression
1 fneq2 4931 . . 3  F  Fn  F  Fn
21anbi1d 438 . 2  F  Fn  ran  F  C  F  Fn  ran  F  C
3 df-fo 4851 . 2  F : -onto-> C  F  Fn  ran  F  C
4 df-fo 4851 . 2  F : -onto-> C  F  Fn  ran  F  C
52, 3, 43bitr4g 212 1  F : -onto-> C  F : -onto-> C
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-fn 4848  df-fo 4851
This theorem is referenced by:  f1oeq2  5061  foeq123d  5065  tposfo  5827
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