Theorem nfoprab1

Description: The abstraction variables in an operation class abstraction are not free. (Contributed by NM, 25-Apr-1995) (Revised by David Abernethy, 19-Jun-2012)

	Ref	Expression
Assertion	nfoprab1	⊢ Ⅎ 𝑥 { ⟨ ⟨ 𝑥 , 𝑦 ⟩ , 𝑧 ⟩ ∣ 𝜑 }

Proof

Step	Hyp	Ref	Expression
1		df-oprab	⊢ { ⟨ ⟨ 𝑥 , 𝑦 ⟩ , 𝑧 ⟩ ∣ 𝜑 } = { 𝑤 ∣ ∃ 𝑥 ∃ 𝑦 ∃ 𝑧 ( 𝑤 = ⟨ ⟨ 𝑥 , 𝑦 ⟩ , 𝑧 ⟩ ∧ 𝜑 ) }
2		nfe1	⊢ Ⅎ 𝑥 ∃ 𝑥 ∃ 𝑦 ∃ 𝑧 ( 𝑤 = ⟨ ⟨ 𝑥 , 𝑦 ⟩ , 𝑧 ⟩ ∧ 𝜑 )
3	2	nfab	⊢ Ⅎ 𝑥 { 𝑤 ∣ ∃ 𝑥 ∃ 𝑦 ∃ 𝑧 ( 𝑤 = ⟨ ⟨ 𝑥 , 𝑦 ⟩ , 𝑧 ⟩ ∧ 𝜑 ) }
4	1 3	nfcxfr	⊢ Ⅎ 𝑥 { ⟨ ⟨ 𝑥 , 𝑦 ⟩ , 𝑧 ⟩ ∣ 𝜑 }