Theorem norcom

Description: The connector -\/ is commutative. (Contributed by Remi, 25-Oct-2023) (Proof shortened by Wolf Lammen, 23-Apr-2024)

	Ref	Expression
Assertion	norcom	⊢ ( ( 𝜑 ⊽ 𝜓 ) ↔ ( 𝜓 ⊽ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		df-nor	⊢ ( ( 𝜑 ⊽ 𝜓 ) ↔ ¬ ( 𝜑 ∨ 𝜓 ) )
2		orcom	⊢ ( ( 𝜑 ∨ 𝜓 ) ↔ ( 𝜓 ∨ 𝜑 ) )
3	1 2	xchbinx	⊢ ( ( 𝜑 ⊽ 𝜓 ) ↔ ¬ ( 𝜓 ∨ 𝜑 ) )
4		df-nor	⊢ ( ( 𝜓 ⊽ 𝜑 ) ↔ ¬ ( 𝜓 ∨ 𝜑 ) )
5	3 4	bitr4i	⊢ ( ( 𝜑 ⊽ 𝜓 ) ↔ ( 𝜓 ⊽ 𝜑 ) )