Theorem eqeltrdi

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

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

Proof

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