Theorem pm4.81 355

Description: Theorem *4.81 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.81	⊢ ((¬ φ → φ) ↔ φ)

Proof of Theorem pm4.81

Step	Hyp	Ref	Expression
1		pm2.18 102	. 2 ⊢ ((¬ φ → φ) → φ)
2		pm2.24 101	. 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)