Theorem ceqsexvOLD

Description: Obsolete version of ceqsexv as of 12-Oct-2024. (Contributed by NM, 2-Mar-1995) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	ceqsexvOLD.1	⊢ 𝐴 ∈ V
	ceqsexvOLD.2	⊢ ( 𝑥 = 𝐴 → ( 𝜑 ↔ 𝜓 ) )
Assertion	ceqsexvOLD	⊢ ( ∃ 𝑥 ( 𝑥 = 𝐴 ∧ 𝜑 ) ↔ 𝜓 )

Proof

Step	Hyp	Ref	Expression
1		ceqsexvOLD.1	⊢ 𝐴 ∈ V
2		ceqsexvOLD.2	⊢ ( 𝑥 = 𝐴 → ( 𝜑 ↔ 𝜓 ) )
3		nfv	⊢ Ⅎ 𝑥 𝜓
4	3 1 2	ceqsex	⊢ ( ∃ 𝑥 ( 𝑥 = 𝐴 ∧ 𝜑 ) ↔ 𝜓 )