Theorem dmmpo

Description: 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	dmmpo	|- dom F = ( 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	1 2	fnmpoi	|- F Fn ( A X. B )
4		fndm	|- ( F Fn ( A X. B ) -> dom F = ( A X. B ) )
5	3 4	ax-mp	|- dom F = ( A X. B )