Theorem nornot 1538

Description: ¬ is expressible via ⊽. (Contributed by Remi, 25-Oct-2023.) (Proof shortened by Wolf Lammen, 8-Dec-2023.)

Assertion

Ref	Expression
nornot	⊢ (¬ 𝜑 ↔ (𝜑 ⊽ 𝜑))

Proof of Theorem nornot

Step	Hyp	Ref	Expression
1		df-nor 1536	. . 3 ⊢ ((𝜑 ⊽ 𝜑) ↔ ¬ (𝜑 ∨ 𝜑))
2		oridm 910	. . 3 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)
3	1, 2	xchbinx 335	. 2 ⊢ ((𝜑 ⊽ 𝜑) ↔ ¬ 𝜑)
4	3	bicomi 225	1 ⊢ (¬ 𝜑 ↔ (𝜑 ⊽ 𝜑))

Syntax hints:  ¬ wn 3   ↔ wb 207   ∨ wo 853   ⊽ wnor 1535

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 208  df-or 854  df-nor 1536

This theorem is referenced by:  noran  1539  noror  1540