Theorem pm2.54 866

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 862	. 2 ⊢ ((𝜑 ∨ 𝜓) ↔ (¬ 𝜑 → 𝜓))
2	1	biimpri 231	1 ⊢ ((¬ 𝜑 → 𝜓) → (𝜑 ∨ 𝜓))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  orrd  877  orim12dALT  925  tsbi3  38987