Theorem eqeltrid

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

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

Proof

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