Theorem nornot 1523

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 1520	. . 3 ⊢ ((𝜑 ⊽ 𝜑) ↔ ¬ (𝜑 ∨ 𝜑))
2		oridm 901	. . 3 ⊢ ((𝜑 ∨ 𝜑) ↔ 𝜑)
3	1, 2	xchbinx 336	. 2 ⊢ ((𝜑 ⊽ 𝜑) ↔ ¬ 𝜑)
4	3	bicomi 226	1 ⊢ (¬ 𝜑 ↔ (𝜑 ⊽ 𝜑))

Syntax hints:  ¬ wn 3   ↔ wb 208   ∨ wo 843   ⊽ wnor 1519

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 209  df-or 844  df-nor 1520

This theorem is referenced by:  noran  1525  noranOLD  1526  noror  1527  nororOLD  1528