Theorem noror 1563

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 1559	. . 3 ⊢ ((𝜑 ⊽ 𝜓) ↔ ¬ (𝜑 ∨ 𝜓))
2	1	con2bii 360	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ ¬ (𝜑 ⊽ 𝜓))
3		nornot 1561	. 2 ⊢ (¬ (𝜑 ⊽ 𝜓) ↔ ((𝜑 ⊽ 𝜓) ⊽ (𝜑 ⊽ 𝜓)))
4	2, 3	bitri 278	1 ⊢ ((𝜑 ∨ 𝜓) ↔ ((𝜑 ⊽ 𝜓) ⊽ (𝜑 ⊽ 𝜓)))

This proof depends on syntax axioms:  ¬ wn 3   ↔ wb 209   ∨ wo 861   ⊽ wnor 1558

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862  df-nor 1559

This theorem is used by: (None)