Theorem fmpttd

Description: Version of fmptd with inlined definition. Domain and codomain of the mapping operation; deduction form. (Contributed by Glauco Siliprandi, 23-Oct-2021) (Proof shortened by BJ, 16-Aug-2022)

	Ref	Expression
Hypothesis	fmpttd.1	|- ( ( ph /\ x e. A ) -> B e. C )
Assertion	fmpttd	|- ( ph -> ( x e. A |-> B ) : A --> C )

Proof

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