Theorem nfn

Description: Inference associated with nfnt . (Contributed by Mario Carneiro, 11-Aug-2016) df-nf changed. (Revised by Wolf Lammen, 18-Sep-2021)

	Ref	Expression
Hypothesis	nfn.1	⊢ Ⅎ 𝑥 𝜑
Assertion	nfn	⊢ Ⅎ 𝑥 ¬ 𝜑

Proof

Step	Hyp	Ref	Expression
1		nfn.1	⊢ Ⅎ 𝑥 𝜑
2		nfnt	⊢ ( Ⅎ 𝑥 𝜑 → Ⅎ 𝑥 ¬ 𝜑 )
3	1 2	ax-mp	⊢ Ⅎ 𝑥 ¬ 𝜑