Theorem pm2.42 772

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		pm2.21 612	. 2 ⊢ (¬ 𝜑 → (𝜑 → 𝜓))
2		id 19	. 2 ⊢ ((𝜑 → 𝜓) → (𝜑 → 𝜓))
3	1, 2	jaoi 711	1 ⊢ ((¬ 𝜑 ∨ (𝜑 → 𝜓)) → (𝜑 → 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 703

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in2 610  ax-io 704

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)