Theorem eqeltrrdi

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

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

Proof

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