Theorem fofun 5591

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

Step	Hyp	Ref	Expression
1		fof 5590	. 2 |- ( F : A -onto-> B -> F : A --> B )
2		ffun 5511	. 2 |- ( F : A --> B -> Fun F )
3	1, 2	syl 14	1 |- ( F : A -onto-> B -> Fun F )

Syntax hints:   -> wi 4   Fun wfun 5346   -->wf 5348   -onto->wfo 5350

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2214

This theorem depends on definitions:  df-bi 117  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-in 3217  df-ss 3224  df-fn 5355  df-f 5356  df-fo 5358

This theorem is referenced by:  foimacnv  5632  resdif  5636  fococnv2  5640  focdmex  6308  ctssdccl  7402  suplocexprlem2b  8029  suplocexprlemmu  8033  suplocexprlemdisj  8035  suplocexprlemloc  8036  suplocexprlemub  8038  suplocexprlemlub  8039  ennnfonelemex  13165  ctinf  13181