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Theorem fofun 5633
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 5632 . 2  |-  ( F : A -onto-> B  ->  F : A --> B )
2 ffun 5573 . 2  |-  ( F : A --> B  ->  Fun  F )
31, 2syl 16 1  |-  ( F : A -onto-> B  ->  Fun  F )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   Fun wfun 5424   -->wf 5426   -onto->wfo 5428
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2430  df-cleq 2436  df-clel 2439  df-in 3347  df-ss 3354  df-fn 5433  df-f 5434  df-fo 5436
This theorem is referenced by:  foimacnv  5670  resdif  5673  fococnv2  5678  fornex  6558  fodomfi2  8242  fin1a2lem7  8587  brdom3  8707  1stf1  15014  1stf2  15015  2ndf1  15017  2ndf2  15018  1stfcl  15019  2ndfcl  15020  qtopcld  19298  qtopcmap  19304  elfm3  19535  bcthlem4  20850  uniiccdif  21070  grporn  23711  subgores  23803  xppreima  25976  bdayfun  27829  ovoliunnfl  28445  voliunnfl  28447
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