Theorem norcomOLD

Description: Obsolete version of norcom as of 23-Apr-2024. (Contributed by Remi, 25-Oct-2023) (Proof modification is discouraged.) (New usage is discouraged.)

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

Proof

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