Theorem 3eltr4i

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

	Ref	Expression
Hypotheses	3eltr4i.1	$$⊢A\in B$$
	3eltr4i.2	$$⊢C=A$$
	3eltr4i.3	$$⊢D=B$$
Assertion	3eltr4i	$$⊢C\in D$$

Proof

Step	Hyp	Ref	Expression
1		3eltr4i.1	$$⊢A\in B$$
2		3eltr4i.2	$$⊢C=A$$
3		3eltr4i.3	$$⊢D=B$$
4	1 3	eleqtrri	$$⊢A\in D$$
5	2 4	eqeltri	$$⊢C\in D$$