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Theorem dffn4 5055
Description: A function maps onto its range. (Contributed by NM, 10-May-1998.)
Assertion
Ref Expression
dffn4  F  Fn  F : -onto-> ran  F

Proof of Theorem dffn4
StepHypRef Expression
1 eqid 2037 . . 3  ran  F  ran  F
21biantru 286 . 2  F  Fn  F  Fn  ran  F  ran  F
3 df-fo 4851 . 2  F : -onto-> ran  F  F  Fn  ran  F  ran  F
42, 3bitr4i 176 1  F  Fn  F : -onto-> ran  F
Colors of variables: wff set class
Syntax hints:   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-gen 1335  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-fo 4851
This theorem is referenced by:  funforn  5056  ffoss  5101  tposf2  5824
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