Theorem mptex

Description: If the domain of a function given by maps-to notation is a set, the function is a set. Inference version of mptexg . (Contributed by NM, 22-Apr-2005) (Revised by Mario Carneiro, 20-Dec-2013)

	Ref	Expression
Hypothesis	mptex.1	$$⊢A\in \mathrm{V}$$
Assertion	mptex	$$⊢\left(x\in A⟼B\right)\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		mptex.1	$$⊢A\in \mathrm{V}$$
2		mptexg	$$⊢A\in \mathrm{V}\to \left(x\in A⟼B\right)\in \mathrm{V}$$
3	1 2	ax-mp	$$⊢\left(x\in A⟼B\right)\in \mathrm{V}$$