Theorem nornot

Description: -. is expressible via -\/ . (Contributed by Remi, 25-Oct-2023) (Proof shortened by Wolf Lammen, 8-Dec-2023)

	Ref	Expression
Assertion	nornot	⊢ ( ¬ 𝜑 ↔ ( 𝜑 ⊽ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		df-nor	⊢ ( ( 𝜑 ⊽ 𝜑 ) ↔ ¬ ( 𝜑 ∨ 𝜑 ) )
2		oridm	⊢ ( ( 𝜑 ∨ 𝜑 ) ↔ 𝜑 )
3	1 2	xchbinx	⊢ ( ( 𝜑 ⊽ 𝜑 ) ↔ ¬ 𝜑 )
4	3	bicomi	⊢ ( ¬ 𝜑 ↔ ( 𝜑 ⊽ 𝜑 ) )