Theorem pm2.54 363

Description: Theorem *2.54 of [WhiteheadRussell] p. 107. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.54	⊢ ((¬ φ → ψ) → (φ ∨ ψ))

Proof of Theorem pm2.54

Step	Hyp	Ref	Expression
1		df-or 359	. 2 ⊢ ((φ ∨ ψ) ↔ (¬ φ → ψ))
2	1	biimpri 197	1 ⊢ ((¬ 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:  orrd  367