Theorem eleqtrid

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

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

Proof

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