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	$$⊢\forall x\neg \phi \to Ⅎx\phi$$

Proof

Step	Hyp	Ref	Expression
1		alnex	$$⊢\forall x\neg \phi \leftrightarrow \neg \exists x\phi$$
2		nfntht	$$⊢\neg \exists x\phi \to Ⅎx\phi$$
3	1 2	sylbi	$$⊢\forall x\neg \phi \to Ⅎx\phi$$