Theorem fofun 5611

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 5610	. 2 |- ( F : A -onto-> B -> F : A --> B )
2		ffun 5531	. 2 |- ( F : A --> B -> Fun F )
3	1, 2	syl 14	1 |- ( F : A -onto-> B -> Fun F )

Syntax hints:   -> wi 4   Fun wfun 5366   -->wf 5368   -onto->wfo 5370

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 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-11 1559  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-in 3226  df-ss 3233  df-fn 5375  df-f 5376  df-fo 5378

This theorem is referenced by:  foimacnv  5652  resdif  5656  fococnv2  5660  focdmex  6334  ctssdccl  7441  suplocexprlem2b  8071  suplocexprlemmu  8075  suplocexprlemdisj  8077  suplocexprlemloc  8078  suplocexprlemub  8080  suplocexprlemlub  8081  ennnfonelemex  13283  ctinf  13299