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	$$⊢\left(\phi \wedge x\in A\right)\to B\in C$$
Assertion	fmpttd	$$⊢\phi \to \left(x\in A⟼B\right):A⟶C$$

Proof

Step	Hyp	Ref	Expression
1		fmpttd.1	$$⊢\left(\phi \wedge x\in A\right)\to B\in C$$
2		eqid	$$⊢\left(x\in A⟼B\right)=\left(x\in A⟼B\right)$$
3	1 2	fmptd	$$⊢\phi \to \left(x\in A⟼B\right):A⟶C$$