Theorem mpteq2dv

Description: An equality inference for the maps-to notation. (Contributed by Mario Carneiro, 23-Aug-2014)

	Ref	Expression
Hypothesis	mpteq2dv.1	$$⊢\phi \to B=C$$
Assertion	mpteq2dv	$$⊢\phi \to \left(x\in A⟼B\right)=\left(x\in A⟼C\right)$$

Proof

Step	Hyp	Ref	Expression
1		mpteq2dv.1	$$⊢\phi \to B=C$$
2	1	adantr	$$⊢\left(\phi \wedge x\in A\right)\to B=C$$
3	2	mpteq2dva	$$⊢\phi \to \left(x\in A⟼B\right)=\left(x\in A⟼C\right)$$