Theorem norcomOLD 1525

Description: Obsolete version of norcom 1524 as of 23-Apr-2024. (Contributed by Remi, 25-Oct-2023.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

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

Proof of Theorem norcomOLD

Step	Hyp	Ref	Expression
1		orcom 866	. . 3 ⊢ ((𝜑 ∨ 𝜓) ↔ (𝜓 ∨ 𝜑))
2	1	notbii 319	. 2 ⊢ (¬ (𝜑 ∨ 𝜓) ↔ ¬ (𝜓 ∨ 𝜑))
3		df-nor 1523	. 2 ⊢ ((𝜑 ⊽ 𝜓) ↔ ¬ (𝜑 ∨ 𝜓))
4		df-nor 1523	. 2 ⊢ ((𝜓 ⊽ 𝜑) ↔ ¬ (𝜓 ∨ 𝜑))
5	2, 3, 4	3bitr4i 302	1 ⊢ ((𝜑 ⊽ 𝜓) ↔ (𝜓 ⊽ 𝜑))

Syntax hints:  ¬ wn 3   ↔ wb 205   ∨ wo 843   ⊽ wnor 1522

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-or 844  df-nor 1523

This theorem is referenced by: (None)