Theorem fnmpoi

Description: Functionality and domain of a class given by the maps-to notation. (Contributed by FL, 17-May-2010)

	Ref	Expression
Hypotheses	fmpo.1	|- F = ( x e. A , y e. B |-> C )
	fnmpoi.2	|- C e. _V
Assertion	fnmpoi	|- F Fn ( A X. B )

Proof

Step	Hyp	Ref	Expression
1		fmpo.1	|- F = ( x e. A , y e. B |-> C )
2		fnmpoi.2	|- C e. _V
3	2	rgen2w	|- A. x e. A A. y e. B C e. _V
4	1	fnmpo	|- ( A. x e. A A. y e. B C e. _V -> F Fn ( A X. B ) )
5	3 4	ax-mp	|- F Fn ( A X. B )