Theorem mptexd

Description: If the domain of a function given by maps-to notation is a set, the function is a set. Deduction version of mptexg . (Contributed by Glauco Siliprandi, 24-Dec-2020)

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

Proof

Step	Hyp	Ref	Expression
1		mptexd.1	$$⊢\phi \to A\in V$$
2		mptexg	$$⊢A\in V\to \left(x\in A⟼B\right)\in \mathrm{V}$$
3	1 2	syl	$$⊢\phi \to \left(x\in A⟼B\right)\in \mathrm{V}$$