Theorem noror 1533

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

Assertion

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

Proof of Theorem noror

Step	Hyp	Ref	Expression
1		df-nor 1528	. . 3 ⊢ ((𝜑 ⊽ 𝜓) ↔ ¬ (𝜑 ∨ 𝜓))
2	1	con2bii 357	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ ¬ (𝜑 ⊽ 𝜓))
3		nornot 1531	. 2 ⊢ (¬ (𝜑 ⊽ 𝜓) ↔ ((𝜑 ⊽ 𝜓) ⊽ (𝜑 ⊽ 𝜓)))
4	2, 3	bitri 274	1 ⊢ ((𝜑 ∨ 𝜓) ↔ ((𝜑 ⊽ 𝜓) ⊽ (𝜑 ⊽ 𝜓)))

Syntax hints:  ¬ wn 3   ↔ wb 205   ∨ wo 844   ⊽ wnor 1527

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 845  df-nor 1528

This theorem is referenced by: (None)