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	$$⊢\neg \exists x\phi \to Ⅎx\phi$$

Proof

Step	Hyp	Ref	Expression
1		pm2.21	$$⊢\neg \exists x\phi \to \left(\exists x\phi \to \forall x\phi \right)$$
2	1	nfd	$$⊢\neg \exists x\phi \to Ⅎx\phi$$