Theorem 3eltr3i

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

	Ref	Expression
Hypotheses	3eltr3i.1	$$⊢A\in B$$
	3eltr3i.2	$$⊢A=C$$
	3eltr3i.3	$$⊢B=D$$
Assertion	3eltr3i	$$⊢C\in D$$

Proof

Step	Hyp	Ref	Expression
1		3eltr3i.1	$$⊢A\in B$$
2		3eltr3i.2	$$⊢A=C$$
3		3eltr3i.3	$$⊢B=D$$
4	1 3	eleqtri	$$⊢A\in D$$
5	2 4	eqeltrri	$$⊢C\in D$$