Theorem eqeltrrid

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

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

Proof

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