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Theorem fofun 5468
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 5467 . 2  |-  ( F : A -onto-> B  ->  F : A --> B )
2 ffun 5407 . 2  |-  ( F : A --> B  ->  Fun  F )
31, 2syl 15 1  |-  ( F : A -onto-> B  ->  Fun  F )
Colors of variables: wff set class
Syntax hints:    -> wi 4   Fun wfun 5265   -->wf 5267   -onto->wfo 5269
This theorem is referenced by:  foimacnv  5506  resdif  5510  fococnv2  5515  fornex  5766  fodomfi2  7703  fin1a2lem7  8048  brdom3  8169  1stf1  13982  1stf2  13983  2ndf1  13985  2ndf2  13986  1stfcl  13987  2ndfcl  13988  qtopcld  17420  qtopcmap  17426  elfm3  17661  bcthlem4  18765  uniiccdif  18949  grporn  20895  subgores  20987  xppreima  23226  bdayfun  24401  ovoliunnfl  25001  imfstnrelc  25184  domrancur1clem  25304  domrancur1c  25305  svs2  25590
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-in 3172  df-ss 3179  df-fn 5274  df-f 5275  df-fo 5277
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