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Theorem fofun 5316
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 5315 . 2  |-  ( F : A -onto-> B  ->  F : A --> B )
2 ffun 5245 . 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 5087   -->wf 5089   -onto->wfo 5091
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-11 1469  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-in 3047  df-ss 3054  df-fn 5096  df-f 5097  df-fo 5099
This theorem is referenced by:  foimacnv  5353  resdif  5357  fococnv2  5361  fornex  5981  ctssdccl  6964  suplocexprlem2b  7490  suplocexprlemmu  7494  suplocexprlemdisj  7496  suplocexprlemloc  7497  suplocexprlemub  7499  suplocexprlemlub  7500  ennnfonelemex  11854  ctinf  11870
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