Theorem 3eltr3d

Description: Substitution of equal classes into membership relation. (Contributed by Mario Carneiro, 6-Jan-2017)

	Ref	Expression
Hypotheses	3eltr3d.1	|- ( ph -> A e. B )
	3eltr3d.2	|- ( ph -> A = C )
	3eltr3d.3	|- ( ph -> B = D )
Assertion	3eltr3d	|- ( ph -> C e. D )

Proof

Step	Hyp	Ref	Expression
1		3eltr3d.1	|- ( ph -> A e. B )
2		3eltr3d.2	|- ( ph -> A = C )
3		3eltr3d.3	|- ( ph -> B = D )
4	1 3	eleqtrd	|- ( ph -> A e. D )
5	2 4	eqeltrrd	|- ( ph -> C e. D )