Theorem nfntht

Description: Closed form of nfnth . (Contributed by BJ, 16-Sep-2021) (Proof shortened by Wolf Lammen, 4-Sep-2022)

	Ref	Expression
Assertion	nfntht	⊢ ( ¬ ∃ 𝑥 𝜑 → Ⅎ 𝑥 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		pm2.21	⊢ ( ¬ ∃ 𝑥 𝜑 → ( ∃ 𝑥 𝜑 → ∀ 𝑥 𝜑 ) )
2	1	nfd	⊢ ( ¬ ∃ 𝑥 𝜑 → Ⅎ 𝑥 𝜑 )