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Theorem fofun 5234
Description: An onto mapping is a function. (Contributed by NM, 29-Mar-2008.)
Assertion
Ref Expression
fofun  |-  ( F : A -onto-> B  ->  Fun  F )

Proof of Theorem fofun
StepHypRef Expression
1 fof 5233 . 2  |-  ( F : A -onto-> B  ->  F : A --> B )
2 ffun 5164 . 2  |-  ( F : A --> B  ->  Fun  F )
31, 2syl 14 1  |-  ( F : A -onto-> B  ->  Fun  F )
Colors of variables: wff set class
Syntax hints:    -> wi 4   Fun wfun 5009   -->wf 5011   -onto->wfo 5013
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-in 3005  df-ss 3012  df-fn 5018  df-f 5019  df-fo 5021
This theorem is referenced by:  foimacnv  5271  resdif  5275  fococnv2  5279  fornex  5886
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