Theorem eleqtri

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

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

Proof

Step	Hyp	Ref	Expression
1		eleqtri.1	⊢ 𝐴 ∈ 𝐵
2		eleqtri.2	⊢ 𝐵 = 𝐶
3	2	eleq2i	⊢ ( 𝐴 ∈ 𝐵 ↔ 𝐴 ∈ 𝐶 )
4	1 3	mpbi	⊢ 𝐴 ∈ 𝐶