Theorem eleq2i

Description: Inference from equality to equivalence of membership. (Contributed by NM, 26-May-1993)

	Ref	Expression
Hypothesis	eleq1i.1	⊢ 𝐴 = 𝐵
Assertion	eleq2i	⊢ ( 𝐶 ∈ 𝐴 ↔ 𝐶 ∈ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		eleq1i.1	⊢ 𝐴 = 𝐵
2		eleq2	⊢ ( 𝐴 = 𝐵 → ( 𝐶 ∈ 𝐴 ↔ 𝐶 ∈ 𝐵 ) )
3	1 2	ax-mp	⊢ ( 𝐶 ∈ 𝐴 ↔ 𝐶 ∈ 𝐵 )