Theorem fofun 5499

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 5498	. 2 |- ( F : A -onto-> B -> F : A --> B )
2		ffun 5428	. 2 |- ( F : A --> B -> Fun F )
3	1, 2	syl 14	1 |- ( F : A -onto-> B -> Fun F )

Syntax hints:   -> wi 4   Fun wfun 5265   -->wf 5267   -onto->wfo 5269

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-11 1529  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-in 3172  df-ss 3179  df-fn 5274  df-f 5275  df-fo 5277

This theorem is referenced by:  foimacnv  5540  resdif  5544  fococnv2  5548  focdmex  6200  ctssdccl  7213  suplocexprlem2b  7827  suplocexprlemmu  7831  suplocexprlemdisj  7833  suplocexprlemloc  7834  suplocexprlemub  7836  suplocexprlemlub  7837  ennnfonelemex  12785  ctinf  12801