Theorem pm4.8 398

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		pm2.01 190	. 2 ⊢ ((𝜑 → ¬ 𝜑) → ¬ 𝜑)
2		ax-1 6	. 2 ⊢ (¬ 𝜑 → (𝜑 → ¬ 𝜑))
3	1, 2	impbii 212	1 ⊢ ((𝜑 → ¬ 𝜑) ↔ ¬ 𝜑)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ↔ wb 209

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210

This theorem is used by:  nannot  1529  ifpimimb  44263