Theorem fmptd2f

Description: Domain and codomain of the mapping operation; deduction form. (Contributed by Glauco Siliprandi, 23-Oct-2021)

	Ref	Expression
Hypotheses	fmptd2f.1	|- F/ x ph
	fmptd2f.2	|- ( ( ph /\ x e. A ) -> B e. C )
Assertion	fmptd2f	|- ( ph -> ( x e. A |-> B ) : A --> C )

Proof

Step	Hyp	Ref	Expression
1		fmptd2f.1	|- F/ x ph
2		fmptd2f.2	|- ( ( ph /\ x e. A ) -> B e. C )
3		eqid	|- ( x e. A |-> B ) = ( x e. A |-> B )
4	1 2 3	fmptdf	|- ( ph -> ( x e. A |-> B ) : A --> C )