Theorem mpteq2dva

Description: Slightly more general equality inference for the maps-to notation. (Contributed by Scott Fenton, 25-Apr-2012) Remove dependency on ax-10 . (Revised by SN, 11-Nov-2024)

	Ref	Expression
Hypothesis	mpteq2dva.1	$$⊢\left(\phi \wedge x\in A\right)\to B=C$$
Assertion	mpteq2dva	$$⊢\phi \to \left(x\in A⟼B\right)=\left(x\in A⟼C\right)$$

Proof

Step	Hyp	Ref	Expression
1		mpteq2dva.1	$$⊢\left(\phi \wedge x\in A\right)\to B=C$$
2		eqidd	$$⊢\phi \to A=A$$
3	2 1	mpteq12dva	$$⊢\phi \to \left(x\in A⟼B\right)=\left(x\in A⟼C\right)$$