Theorem eleqtrrdi

Description: A membership and equality inference. (Contributed by NM, 24-Apr-2005)

	Ref	Expression
Hypotheses	eleqtrrdi.1	|- ( ph -> A e. B )
	eleqtrrdi.2	|- C = B
Assertion	eleqtrrdi	|- ( ph -> A e. C )

Proof

Step	Hyp	Ref	Expression
1		eleqtrrdi.1	|- ( ph -> A e. B )
2		eleqtrrdi.2	|- C = B
3	2	eqcomi	|- B = C
4	1 3	eleqtrdi	|- ( ph -> A e. C )