Theorem fof

Description: An onto mapping is a mapping. (Contributed by NM, 3-Aug-1994)

	Ref	Expression
Assertion	fof	|- ( F : A -onto-> B -> F : A --> B )

Proof

Step	Hyp	Ref	Expression
1		eqimss	|- ( ran F = B -> ran F C_ B )
2	1	anim2i	|- ( ( F Fn A /\ ran F = B ) -> ( F Fn A /\ ran F C_ B ) )
3		df-fo	|- ( F : A -onto-> B <-> ( F Fn A /\ ran F = B ) )
4		df-f	|- ( F : A --> B <-> ( F Fn A /\ ran F C_ B ) )
5	2 3 4	3imtr4i	|- ( F : A -onto-> B -> F : A --> B )