Theorem pm4.8 354

Description: Theorem *4.8 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.8	⊢ ((φ → ¬ φ) ↔ ¬ φ)

Proof of Theorem pm4.8

Step	Hyp	Ref	Expression
1		pm2.01 160	. 2 ⊢ ((φ → ¬ φ) → ¬ φ)
2		ax-1 6	. 2 ⊢ (¬ φ → (φ → ¬ φ))
3	1, 2	impbii 180	1 ⊢ ((φ → ¬ φ) ↔ ¬ φ)

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 176

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 177

This theorem is referenced by: (None)