Theorem fofun 5557

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 5556	. 2 |- ( F : A -onto-> B -> F : A --> B )
2		ffun 5482	. 2 |- ( F : A --> B -> Fun F )
3	1, 2	syl 14	1 |- ( F : A -onto-> B -> Fun F )

Syntax hints:   -> wi 4   Fun wfun 5318   -->wf 5320   -onto->wfo 5322

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 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-11 1552  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-in 3204  df-ss 3211  df-fn 5327  df-f 5328  df-fo 5330

This theorem is referenced by:  foimacnv  5598  resdif  5602  fococnv2  5606  focdmex  6272  ctssdccl  7301  suplocexprlem2b  7924  suplocexprlemmu  7928  suplocexprlemdisj  7930  suplocexprlemloc  7931  suplocexprlemub  7933  suplocexprlemlub  7934  ennnfonelemex  13025  ctinf  13041