Theorem 3eltr4i

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

	Ref	Expression
Hypotheses	3eltr4i.1	⊢ 𝐴 ∈ 𝐵
	3eltr4i.2	⊢ 𝐶 = 𝐴
	3eltr4i.3	⊢ 𝐷 = 𝐵
Assertion	3eltr4i	⊢ 𝐶 ∈ 𝐷

Proof

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