Theorem fofun 5521

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 5520	. 2 |- ( F : A -onto-> B -> F : A --> B )
2		ffun 5448	. 2 |- ( F : A --> B -> Fun F )
3	1, 2	syl 14	1 |- ( F : A -onto-> B -> Fun F )

Syntax hints:   -> wi 4   Fun wfun 5284   -->wf 5286   -onto->wfo 5288

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 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-11 1530  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-in 3180  df-ss 3187  df-fn 5293  df-f 5294  df-fo 5296

This theorem is referenced by:  foimacnv  5562  resdif  5566  fococnv2  5570  focdmex  6223  ctssdccl  7239  suplocexprlem2b  7862  suplocexprlemmu  7866  suplocexprlemdisj  7868  suplocexprlemloc  7869  suplocexprlemub  7871  suplocexprlemlub  7872  ennnfonelemex  12900  ctinf  12916