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Metamath Proof Explorer

Theorem nfntht2

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

		Ref	Expression
	Assertion	nfntht2	⊢ ( ∀ 𝑥 ¬ 𝜑 → Ⅎ 𝑥 𝜑 )

Step	Hyp	Ref	Expression
1		alnex	⊢ ( ∀ 𝑥 ¬ 𝜑 ↔ ¬ ∃ 𝑥 𝜑 )
2		nfntht	⊢ ( ¬ ∃ 𝑥 𝜑 → Ⅎ 𝑥 𝜑 )
3	1 2	sylbi	⊢ ( ∀ 𝑥 ¬ 𝜑 → Ⅎ 𝑥 𝜑 )