Theorem pm4.8 697

Description: Theorem *4.8 of [WhiteheadRussell] p. 122. This one holds for all propositions, but compare with pm4.81dc 898 which requires a decidability condition. (Contributed by NM, 3-Jan-2005.)

Assertion

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

Proof of Theorem pm4.8

Step	Hyp	Ref	Expression
1		pm2.01 606	. 2 ⊢ ((𝜑 → ¬ 𝜑) → ¬ 𝜑)
2		ax-1 6	. 2 ⊢ (¬ 𝜑 → (𝜑 → ¬ 𝜑))
3	1, 2	impbii 125	1 ⊢ ((𝜑 → ¬ 𝜑) ↔ ¬ 𝜑)

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia2 106  ax-ia3 107  ax-in1 604

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)