Theorem mpteq1d

Description: An equality theorem for the maps-to notation. (Contributed by Mario Carneiro, 11-Jun-2016)

	Ref	Expression
Hypothesis	mpteq1d.1	$$⊢\phi \to A=B$$
Assertion	mpteq1d	$$⊢\phi \to \left(x\in A⟼C\right)=\left(x\in B⟼C\right)$$

Proof

Step	Hyp	Ref	Expression
1		mpteq1d.1	$$⊢\phi \to A=B$$
2		mpteq1	$$⊢A=B\to \left(x\in A⟼C\right)=\left(x\in B⟼C\right)$$
3	1 2	syl	$$⊢\phi \to \left(x\in A⟼C\right)=\left(x\in B⟼C\right)$$