Theorem mo4OLD

Description: Obsolete version of mo4 as of 18-Oct-2023. (Contributed by NM, 26-Jul-1995) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	mo4OLD.1	⊢ ( 𝑥 = 𝑦 → ( 𝜑 ↔ 𝜓 ) )
Assertion	mo4OLD	⊢ ( ∃* 𝑥 𝜑 ↔ ∀ 𝑥 ∀ 𝑦 ( ( 𝜑 ∧ 𝜓 ) → 𝑥 = 𝑦 ) )

Proof

Step	Hyp	Ref	Expression
1		mo4OLD.1	⊢ ( 𝑥 = 𝑦 → ( 𝜑 ↔ 𝜓 ) )
2		nfv	⊢ Ⅎ 𝑥 𝜓
3	2 1	mo4f	⊢ ( ∃* 𝑥 𝜑 ↔ ∀ 𝑥 ∀ 𝑦 ( ( 𝜑 ∧ 𝜓 ) → 𝑥 = 𝑦 ) )