Theorem noror

Description: \/ is expressible via -\/ . (Contributed by Remi, 26-Oct-2023) (Proof shortened by Wolf Lammen, 8-Dec-2023)

	Ref	Expression
Assertion	noror	⊢ ( ( 𝜑 ∨ 𝜓 ) ↔ ( ( 𝜑 ⊽ 𝜓 ) ⊽ ( 𝜑 ⊽ 𝜓 ) ) )

Proof

Step	Hyp	Ref	Expression
1		df-nor	⊢ ( ( 𝜑 ⊽ 𝜓 ) ↔ ¬ ( 𝜑 ∨ 𝜓 ) )
2	1	con2bii	⊢ ( ( 𝜑 ∨ 𝜓 ) ↔ ¬ ( 𝜑 ⊽ 𝜓 ) )
3		nornot	⊢ ( ¬ ( 𝜑 ⊽ 𝜓 ) ↔ ( ( 𝜑 ⊽ 𝜓 ) ⊽ ( 𝜑 ⊽ 𝜓 ) ) )
4	2 3	bitri	⊢ ( ( 𝜑 ∨ 𝜓 ) ↔ ( ( 𝜑 ⊽ 𝜓 ) ⊽ ( 𝜑 ⊽ 𝜓 ) ) )