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	$$⊢F=\left(x\in A,y\in B⟼C\right)$$
	fnmpoi.2	$$⊢C\in \mathrm{V}$$
Assertion	fnmpoi	$$⊢FFn\left(A\times B\right)$$

Proof

Step	Hyp	Ref	Expression
1		fmpo.1	$$⊢F=\left(x\in A,y\in B⟼C\right)$$
2		fnmpoi.2	$$⊢C\in \mathrm{V}$$
3	2	rgen2w	$$⊢\forall x\in A\forall y\in BC\in \mathrm{V}$$
4	1	fnmpo	$$⊢\forall x\in A\forall y\in BC\in \mathrm{V}\to FFn\left(A\times B\right)$$
5	3 4	ax-mp	$$⊢FFn\left(A\times B\right)$$