Theorem 3eltr4g

Description: Substitution of equal classes into membership relation. (Contributed by Mario Carneiro, 6-Jan-2017) (Proof shortened by Wolf Lammen, 23-Nov-2019)

	Ref	Expression
Hypotheses	3eltr4g.1	|- ( ph -> A e. B )
	3eltr4g.2	|- C = A
	3eltr4g.3	|- D = B
Assertion	3eltr4g	|- ( ph -> C e. D )

Proof

Step	Hyp	Ref	Expression
1		3eltr4g.1	|- ( ph -> A e. B )
2		3eltr4g.2	|- C = A
3		3eltr4g.3	|- D = B
4	2 1	eqeltrid	|- ( ph -> C e. B )
5	4 3	eleqtrrdi	|- ( ph -> C e. D )