Theorem eleq2i

Description: Inference from equality to equivalence of membership. (Contributed by NM, 26-May-1993)

	Ref	Expression
Hypothesis	eleq1i.1	|- A = B
Assertion	eleq2i	|- ( C e. A <-> C e. B )

Proof

Step	Hyp	Ref	Expression
1		eleq1i.1	|- A = B
2		eleq2	|- ( A = B -> ( C e. A <-> C e. B ) )
3	1 2	ax-mp	|- ( C e. A <-> C e. B )