Theorem cbvreuvwOLD

Description: Obsolete version of cbvreuvw as of 30-Sep-2024. (Contributed by NM, 5-Apr-2004) (Revised by Gino Giotto, 10-Jan-2024) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	cbvralvw.1	⊢ ( 𝑥 = 𝑦 → ( 𝜑 ↔ 𝜓 ) )
Assertion	cbvreuvwOLD	⊢ ( ∃! 𝑥 ∈ 𝐴 𝜑 ↔ ∃! 𝑦 ∈ 𝐴 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		cbvralvw.1	⊢ ( 𝑥 = 𝑦 → ( 𝜑 ↔ 𝜓 ) )
2		nfv	⊢ Ⅎ 𝑦 𝜑
3		nfv	⊢ Ⅎ 𝑥 𝜓
4	2 3 1	cbvreuw	⊢ ( ∃! 𝑥 ∈ 𝐴 𝜑 ↔ ∃! 𝑦 ∈ 𝐴 𝜓 )