Theorem mpteq1

Description: An equality theorem for the maps-to notation. (Contributed by Mario Carneiro, 16-Dec-2013) (Proof shortened by SN, 11-Nov-2024)

	Ref	Expression
Assertion	mpteq1	$$⊢A=B\to \left(x\in A⟼C\right)=\left(x\in B⟼C\right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢A=B\to A=B$$
2		eqidd	$$⊢A=B\to C=C$$
3	1 2	mpteq12dv	$$⊢A=B\to \left(x\in A⟼C\right)=\left(x\in B⟼C\right)$$