Theorem 3eltr4d

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

	Ref	Expression
Hypotheses	3eltr4d.1	|- ( ph -> A e. B )
	3eltr4d.2	|- ( ph -> C = A )
	3eltr4d.3	|- ( ph -> D = B )
Assertion	3eltr4d	|- ( ph -> C e. D )

Proof

Step	Hyp	Ref	Expression
1		3eltr4d.1	|- ( ph -> A e. B )
2		3eltr4d.2	|- ( ph -> C = A )
3		3eltr4d.3	|- ( ph -> D = B )
4	1 3	eleqtrrd	|- ( ph -> A e. D )
5	2 4	eqeltrd	|- ( ph -> C e. D )