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	⊢ ( ( 𝜑 ⊼ 𝜓 ) ↔ ( ¬ 𝜑 ∨ ¬ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		df-nan	⊢ ( ( 𝜑 ⊼ 𝜓 ) ↔ ¬ ( 𝜑 ∧ 𝜓 ) )
2		ianor	⊢ ( ¬ ( 𝜑 ∧ 𝜓 ) ↔ ( ¬ 𝜑 ∨ ¬ 𝜓 ) )
3	1 2	bitri	⊢ ( ( 𝜑 ⊼ 𝜓 ) ↔ ( ¬ 𝜑 ∨ ¬ 𝜓 ) )