Theorem fofun 5498

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 5497	. 2 |- ( F : A -onto-> B -> F : A --> B )
2		ffun 5427	. 2 |- ( F : A --> B -> Fun F )
3	1, 2	syl 14	1 |- ( F : A -onto-> B -> Fun F )

Syntax hints:   -> wi 4   Fun wfun 5264   -->wf 5266   -onto->wfo 5268

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 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-11 1528  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557  ax-ext 2186

This theorem depends on definitions:  df-bi 117  df-nf 1483  df-sb 1785  df-clab 2191  df-cleq 2197  df-clel 2200  df-in 3171  df-ss 3178  df-fn 5273  df-f 5274  df-fo 5276

This theorem is referenced by:  foimacnv  5539  resdif  5543  fococnv2  5547  focdmex  6199  ctssdccl  7212  suplocexprlem2b  7826  suplocexprlemmu  7830  suplocexprlemdisj  7832  suplocexprlemloc  7833  suplocexprlemub  7835  suplocexprlemlub  7836  ennnfonelemex  12756  ctinf  12772