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Metamath Proof Explorer

Theorem nannot

Description: Negation in terms of alternative denial. (Contributed by Jeff Hoffman, 19-Nov-2007) Use dfnan2 . (Revised by Wolf Lammen, 26-Jun-2020)

		Ref	Expression
	Assertion	nannot	$⊢ \neg φ \leftrightarrow (φ ⊼ φ)$

Proof

Step	Hyp	Ref	Expression
1		dfnan2	$⊢ (φ ⊼ φ) \leftrightarrow (φ \to \neg φ)$
2		pm4.8	$⊢ (φ \to \neg φ) \leftrightarrow \neg φ$
3	1 2	bitr2i	$⊢ \neg φ \leftrightarrow (φ ⊼ φ)$