Theorem eleqtrrd

Description: Deduction that substitutes equal classes into membership. (Contributed by NM, 14-Dec-2004)

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

Proof

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