Theorem fofun 5411

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 5410	. 2 |- ( F : A -onto-> B -> F : A --> B )
2		ffun 5340	. 2 |- ( F : A --> B -> Fun F )
3	1, 2	syl 14	1 |- ( F : A -onto-> B -> Fun F )

Syntax hints:   -> wi 4   Fun wfun 5182   -->wf 5184   -onto->wfo 5186

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 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-11 1494  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-in 3122  df-ss 3129  df-fn 5191  df-f 5192  df-fo 5194

This theorem is referenced by:  foimacnv  5450  resdif  5454  fococnv2  5458  fornex  6083  ctssdccl  7076  suplocexprlem2b  7655  suplocexprlemmu  7659  suplocexprlemdisj  7661  suplocexprlemloc  7662  suplocexprlemub  7664  suplocexprlemlub  7665  ennnfonelemex  12347  ctinf  12363