Theorem fofun 5421

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 5420	. 2 |- ( F : A -onto-> B -> F : A --> B )
2		ffun 5350	. 2 |- ( F : A --> B -> Fun F )
3	1, 2	syl 14	1 |- ( F : A -onto-> B -> Fun F )

Syntax hints:   -> wi 4   Fun wfun 5192   -->wf 5194   -onto->wfo 5196

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-11 1499  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-in 3127  df-ss 3134  df-fn 5201  df-f 5202  df-fo 5204

This theorem is referenced by:  foimacnv  5460  resdif  5464  fococnv2  5468  fornex  6094  ctssdccl  7088  suplocexprlem2b  7676  suplocexprlemmu  7680  suplocexprlemdisj  7682  suplocexprlemloc  7683  suplocexprlemub  7685  suplocexprlemlub  7686  ennnfonelemex  12369  ctinf  12385