Theorem pm2.54 848

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 844	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
2	1	biimpri 230	1 ⊢ ((¬ 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 209  df-or 844

This theorem is referenced by:  orrd  859  orim12dALT  908  tsbi3  35407