Theorem mpteq1iOLD

Description: An equality theorem for the maps-to notation. (Contributed by Glauco Siliprandi, 17-Aug-2020) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	mpteq1i.1	$$⊢A=B$$
Assertion	mpteq1iOLD	$$⊢\left(x\in A⟼C\right)=\left(x\in B⟼C\right)$$

Proof

Step	Hyp	Ref	Expression
1		mpteq1i.1	$$⊢A=B$$
2		mpteq1	$$⊢A=B\to \left(x\in A⟼C\right)=\left(x\in B⟼C\right)$$
3	1 2	ax-mp	$$⊢\left(x\in A⟼C\right)=\left(x\in B⟼C\right)$$