Theorem pm2.42 557

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		pm2.21 100	. 2 ⊢ (¬ φ → (φ → ψ))
2		id 19	. 2 ⊢ ((φ → ψ) → (φ → ψ))
3	1, 2	jaoi 368	1 ⊢ ((¬ φ ∨ (φ → ψ)) → (φ → ψ))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 357

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  df-or 359

This theorem is referenced by: (None)