Theorem pm2.42 939

Description: Theorem *2.42 of [WhiteheadRussell] p. 106. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.42	⊢ ((¬ 𝜑 ∨ (𝜑 → 𝜓)) → (𝜑 → 𝜓))

Proof of Theorem pm2.42

Step	Hyp	Ref	Expression
1		pm2.21 123	. 2 ⊢ (¬ 𝜑 → (𝜑 → 𝜓))
2		id 22	. 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜓))
3	1, 2	jaoi 853	1 ⊢ ((¬ 𝜑 ∨ (𝜑 → 𝜓)) → (𝜑 → 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 843

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 206  df-or 844

This theorem is referenced by: (None)