Theorem relopabv

Description: A class of ordered pairs is a relation. For a version without a disjoint variable condition, but using ax-11 and ax-12 , see relopab . (Contributed by SN, 8-Sep-2024)

	Ref	Expression
Assertion	relopabv	⊢ Rel { ⟨ 𝑥 , 𝑦 ⟩ ∣ 𝜑 }

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ { ⟨ 𝑥 , 𝑦 ⟩ ∣ 𝜑 } = { ⟨ 𝑥 , 𝑦 ⟩ ∣ 𝜑 }
2	1	relopabiv	⊢ Rel { ⟨ 𝑥 , 𝑦 ⟩ ∣ 𝜑 }