Theorem wl-nannot 32478

Description: Show equivalence between negation and the Nicod version. To derive nic-dfneg 1586, apply nanbi 1446. (Contributed by Jeff Hoffman, 19-Nov-2007.) (Revised by Wolf Lammen, 26-Jun-2020.)

Assertion

Ref	Expression
wl-nannot	⊢ (¬ 𝜑 ↔ (𝜑 ⊼ 𝜑))

Proof of Theorem wl-nannot

Step	Hyp	Ref	Expression
1		wl-dfnan2 32475	. 2 ⊢ ((𝜑 ⊼ 𝜑) ↔ (𝜑 → ¬ 𝜑))
2		pm4.8 379	. 2 ⊢ ((𝜑 → ¬ 𝜑) ↔ ¬ 𝜑)
3	1, 2	bitr2i 264	1 ⊢ (¬ 𝜑 ↔ (𝜑 ⊼ 𝜑))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 195   ⊼ wnan 1439

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 196  df-an 385  df-nan 1440

This theorem is referenced by: (None)