Theorem eleqtrri

Description: Substitution of equal classes into membership relation. (Contributed by NM, 15-Jul-1993)

	Ref	Expression
Hypotheses	eleqtrri.1	⊢ 𝐴 ∈ 𝐵
	eleqtrri.2	⊢ 𝐶 = 𝐵
Assertion	eleqtrri	⊢ 𝐴 ∈ 𝐶

Proof

Step	Hyp	Ref	Expression
1		eleqtrri.1	⊢ 𝐴 ∈ 𝐵
2		eleqtrri.2	⊢ 𝐶 = 𝐵
3	2	eqcomi	⊢ 𝐵 = 𝐶
4	1 3	eleqtri	⊢ 𝐴 ∈ 𝐶