Theorem mpteq2i

Description: An equality inference for the maps-to notation. (Contributed by Mario Carneiro, 16-Dec-2013)

	Ref	Expression
Hypothesis	mpteq2i.1	$$⊢B=C$$
Assertion	mpteq2i	$$⊢\left(x\in A⟼B\right)=\left(x\in A⟼C\right)$$

Proof

Step	Hyp	Ref	Expression
1		mpteq2i.1	$$⊢B=C$$
2	1	a1i	$$⊢x\in A\to B=C$$
3	2	mpteq2ia	$$⊢\left(x\in A⟼B\right)=\left(x\in A⟼C\right)$$