Theorem eleqtrri

Description: Substitution of equal classes into membership relation. (Contributed by NM, 15-Jul-1993)

	Ref	Expression
Hypotheses	eleqtrri.1	|- A e. B
	eleqtrri.2	|- C = B
Assertion	eleqtrri	|- A e. C

Proof

Step	Hyp	Ref	Expression
1		eleqtrri.1	|- A e. B
2		eleqtrri.2	|- C = B
3	2	eqcomi	|- B = C
4	1 3	eleqtri	|- A e. C