Theorem nororOLD 1531

Description: Obsolete version of noror 1530 as of 8-Dec-2023. (Contributed by Remi, 26-Oct-2023.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
nororOLD	⊢ ((𝜑 ∨ 𝜓) ↔ ((𝜑 ⊽ 𝜓) ⊽ (𝜑 ⊽ 𝜓)))

Proof of Theorem nororOLD

Step	Hyp	Ref	Expression
1		notnotb 314	. . 3 ⊢ ((𝜑 ∨ 𝜓) ↔ ¬ ¬ (𝜑 ∨ 𝜓))
2		df-nor 1523	. . . 4 ⊢ ((𝜑 ⊽ 𝜓) ↔ ¬ (𝜑 ∨ 𝜓))
3	2	notbii 319	. . 3 ⊢ (¬ (𝜑 ⊽ 𝜓) ↔ ¬ ¬ (𝜑 ∨ 𝜓))
4		nornot 1526	. . 3 ⊢ (¬ (𝜑 ⊽ 𝜓) ↔ ((𝜑 ⊽ 𝜓) ⊽ (𝜑 ⊽ 𝜓)))
5	1, 3, 4	3bitr2ri 299	. 2 ⊢ (((𝜑 ⊽ 𝜓) ⊽ (𝜑 ⊽ 𝜓)) ↔ (𝜑 ∨ 𝜓))
6	5	bicomi 223	1 ⊢ ((𝜑 ∨ 𝜓) ↔ ((𝜑 ⊽ 𝜓) ⊽ (𝜑 ⊽ 𝜓)))

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)