Theorem eleqtrrid

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

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

Proof

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