Theorem fofun 5441

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 5440	. 2 |- ( F : A -onto-> B -> F : A --> B )
2		ffun 5370	. 2 |- ( F : A --> B -> Fun F )
3	1, 2	syl 14	1 |- ( F : A -onto-> B -> Fun F )

Syntax hints:   -> wi 4   Fun wfun 5212   -->wf 5214   -onto->wfo 5216

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 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-in 3137  df-ss 3144  df-fn 5221  df-f 5222  df-fo 5224

This theorem is referenced by:  foimacnv  5481  resdif  5485  fococnv2  5489  focdmex  6118  ctssdccl  7112  suplocexprlem2b  7715  suplocexprlemmu  7719  suplocexprlemdisj  7721  suplocexprlemloc  7722  suplocexprlemub  7724  suplocexprlemlub  7725  ennnfonelemex  12417  ctinf  12433