This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

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	$⊢ Ⅎ x \neg φ$

Step	Hyp	Ref	Expression
1		nfn.1	$⊢ Ⅎ x φ$
2		nfnt	$⊢ Ⅎ x φ \to Ⅎ x \neg φ$
3	1 2	ax-mp	$⊢ Ⅎ x \neg φ$