Theorem fexd

Description: If the domain of a mapping is a set, the function is a set. (Contributed by Glauco Siliprandi, 26-Jun-2021)

	Ref	Expression
Hypotheses	fexd.1	|- ( ph -> F : A --> B )
	fexd.2	|- ( ph -> A e. C )
Assertion	fexd	|- ( ph -> F e. _V )

Proof

Step	Hyp	Ref	Expression
1		fexd.1	|- ( ph -> F : A --> B )
2		fexd.2	|- ( ph -> A e. C )
3		fex	|- ( ( F : A --> B /\ A e. C ) -> F e. _V )
4	1 2 3	syl2anc	|- ( ph -> F e. _V )