Theorem fofun 5560

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 5559	. 2 |- ( F : A -onto-> B -> F : A --> B )
2		ffun 5485	. 2 |- ( F : A --> B -> Fun F )
3	1, 2	syl 14	1 |- ( F : A -onto-> B -> Fun F )

Syntax hints:   -> wi 4   Fun wfun 5320   -->wf 5322   -onto->wfo 5324

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 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-11 1554  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-in 3206  df-ss 3213  df-fn 5329  df-f 5330  df-fo 5332

This theorem is referenced by:  foimacnv  5601  resdif  5605  fococnv2  5609  focdmex  6276  ctssdccl  7309  suplocexprlem2b  7933  suplocexprlemmu  7937  suplocexprlemdisj  7939  suplocexprlemloc  7940  suplocexprlemub  7942  suplocexprlemlub  7943  ennnfonelemex  13034  ctinf  13050