Theorem eleq12i

Description: Inference from equality to equivalence of membership. (Contributed by NM, 31-May-1994)

	Ref	Expression
Hypotheses	eleq1i.1	|- A = B
	eleq12i.2	|- C = D
Assertion	eleq12i	|- ( A e. C <-> B e. D )

Proof

Step	Hyp	Ref	Expression
1		eleq1i.1	|- A = B
2		eleq12i.2	|- C = D
3	2	eleq2i	|- ( A e. C <-> A e. D )
4	1	eleq1i	|- ( A e. D <-> B e. D )
5	3 4	bitri	|- ( A e. C <-> B e. D )