Theorem eleqtrdi

Description: A membership and equality inference. (Contributed by NM, 4-Jan-2006)

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

Proof

Step	Hyp	Ref	Expression
1		eleqtrdi.1	|- ( ph -> A e. B )
2		eleqtrdi.2	|- B = C
3	2	a1i	|- ( ph -> B = C )
4	1 3	eleqtrd	|- ( ph -> A e. C )