Theorem 3eltr3i

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

	Ref	Expression
Hypotheses	3eltr3i.1	|- A e. B
	3eltr3i.2	|- A = C
	3eltr3i.3	|- B = D
Assertion	3eltr3i	|- C e. D

Proof

Step	Hyp	Ref	Expression
1		3eltr3i.1	|- A e. B
2		3eltr3i.2	|- A = C
3		3eltr3i.3	|- B = D
4	1 3	eleqtri	|- A e. D
5	2 4	eqeltrri	|- C e. D