Theorem fofun 5478

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 5477	. 2 |- ( F : A -onto-> B -> F : A --> B )
2		ffun 5407	. 2 |- ( F : A --> B -> Fun F )
3	1, 2	syl 14	1 |- ( F : A -onto-> B -> Fun F )

Syntax hints:   -> wi 4   Fun wfun 5249   -->wf 5251   -onto->wfo 5253

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-in 3160  df-ss 3167  df-fn 5258  df-f 5259  df-fo 5261

This theorem is referenced by:  foimacnv  5519  resdif  5523  fococnv2  5527  focdmex  6169  ctssdccl  7172  suplocexprlem2b  7776  suplocexprlemmu  7780  suplocexprlemdisj  7782  suplocexprlemloc  7783  suplocexprlemub  7785  suplocexprlemlub  7786  ennnfonelemex  12574  ctinf  12590