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	|- ( ph -> A e. V )
Assertion	mptexd	|- ( ph -> ( x e. A |-> B ) e. _V )

Proof

Step	Hyp	Ref	Expression
1		mptexd.1	|- ( ph -> A e. V )
2		mptexg	|- ( A e. V -> ( x e. A |-> B ) e. _V )
3	1 2	syl	|- ( ph -> ( x e. A |-> B ) e. _V )