Theorem fofun 5548

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 5547	. 2 |- ( F : A -onto-> B -> F : A --> B )
2		ffun 5475	. 2 |- ( F : A --> B -> Fun F )
3	1, 2	syl 14	1 |- ( F : A -onto-> B -> Fun F )

Syntax hints:   -> wi 4   Fun wfun 5311   -->wf 5313   -onto->wfo 5315

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 3203  df-ss 3210  df-fn 5320  df-f 5321  df-fo 5323

This theorem is referenced by:  foimacnv  5589  resdif  5593  fococnv2  5597  focdmex  6258  ctssdccl  7274  suplocexprlem2b  7897  suplocexprlemmu  7901  suplocexprlemdisj  7903  suplocexprlemloc  7904  suplocexprlemub  7906  suplocexprlemlub  7907  ennnfonelemex  12980  ctinf  12996