Theorem ceqsexgvOLD

Description: Obsolete version of ceqsexgv as of 1-Dec-2023. (Contributed by NM, 29-Dec-1996) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	ceqsexgv.1	⊢ ( 𝑥 = 𝐴 → ( 𝜑 ↔ 𝜓 ) )
Assertion	ceqsexgvOLD	⊢ ( 𝐴 ∈ 𝑉 → ( ∃ 𝑥 ( 𝑥 = 𝐴 ∧ 𝜑 ) ↔ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		ceqsexgv.1	⊢ ( 𝑥 = 𝐴 → ( 𝜑 ↔ 𝜓 ) )
2		nfv	⊢ Ⅎ 𝑥 𝜓
3	2 1	ceqsexg	⊢ ( 𝐴 ∈ 𝑉 → ( ∃ 𝑥 ( 𝑥 = 𝐴 ∧ 𝜑 ) ↔ 𝜓 ) )