Theorem nanor

Description: Alternative denial in terms of disjunction and negation. This explains the name "alternative denial". (Contributed by BJ, 19-Oct-2022)

	Ref	Expression
Assertion	nanor	$$⊢\left(\phi ⊼\psi \right)\leftrightarrow \left(\neg \phi \vee \neg \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		df-nan	$$⊢\left(\phi ⊼\psi \right)\leftrightarrow \neg \left(\phi \wedge \psi \right)$$
2		ianor	$$⊢\neg \left(\phi \wedge \psi \right)\leftrightarrow \left(\neg \phi \vee \neg \psi \right)$$
3	1 2	bitri	$$⊢\left(\phi ⊼\psi \right)\leftrightarrow \left(\neg \phi \vee \neg \psi \right)$$