Theorem 3eltr4i

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

	Ref	Expression
Hypotheses	3eltr4i.1	|- A e. B
	3eltr4i.2	|- C = A
	3eltr4i.3	|- D = B
Assertion	3eltr4i	|- C e. D

Proof

Step	Hyp	Ref	Expression
1		3eltr4i.1	|- A e. B
2		3eltr4i.2	|- C = A
3		3eltr4i.3	|- D = B
4	1 3	eleqtrri	|- A e. D
5	2 4	eqeltri	|- C e. D