Theorem eleq1i

Description: Inference from equality to equivalence of membership. (Contributed by NM, 21-Jun-1993)

	Ref	Expression
Hypothesis	eleq1i.1	$$⊢A=B$$
Assertion	eleq1i	$$⊢A\in C\leftrightarrow B\in C$$

Proof

Step	Hyp	Ref	Expression
1		eleq1i.1	$$⊢A=B$$
2		eleq1	$$⊢A=B\to \left(A\in C\leftrightarrow B\in C\right)$$
3	1 2	ax-mp	$$⊢A\in C\leftrightarrow B\in C$$