Theorem cbvopab1vOLD

Description: Obsolete version of cbvopab1v as of 17-Nov-2024. (Contributed by NM, 31-Jul-2003) (Proof shortened by Eric Schmidt, 4-Apr-2007) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	cbvopab1vOLD.1	⊢ ( 𝑥 = 𝑧 → ( 𝜑 ↔ 𝜓 ) )
Assertion	cbvopab1vOLD	⊢ { ⟨ 𝑥 , 𝑦 ⟩ ∣ 𝜑 } = { ⟨ 𝑧 , 𝑦 ⟩ ∣ 𝜓 }

Proof

Step	Hyp	Ref	Expression
1		cbvopab1vOLD.1	⊢ ( 𝑥 = 𝑧 → ( 𝜑 ↔ 𝜓 ) )
2		nfv	⊢ Ⅎ 𝑧 𝜑
3		nfv	⊢ Ⅎ 𝑥 𝜓
4	2 3 1	cbvopab1	⊢ { ⟨ 𝑥 , 𝑦 ⟩ ∣ 𝜑 } = { ⟨ 𝑧 , 𝑦 ⟩ ∣ 𝜓 }