Metamath Proof Explorer


Theorem reloprab

Description: An operation class abstraction is a relation. (Contributed by NM, 16-Jun-2004)

Ref Expression
Assertion reloprab Rel { ⟨ ⟨ 𝑥 , 𝑦 ⟩ , 𝑧 ⟩ ∣ 𝜑 }

Proof

Step Hyp Ref Expression
1 dfoprab2 { ⟨ ⟨ 𝑥 , 𝑦 ⟩ , 𝑧 ⟩ ∣ 𝜑 } = { ⟨ 𝑤 , 𝑧 ⟩ ∣ ∃ 𝑥𝑦 ( 𝑤 = ⟨ 𝑥 , 𝑦 ⟩ ∧ 𝜑 ) }
2 1 relopabiv Rel { ⟨ ⟨ 𝑥 , 𝑦 ⟩ , 𝑧 ⟩ ∣ 𝜑 }