Theorem pm5.12 942

Description: Theorem *5.12 of [WhiteheadRussell] p. 123. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.12	⊢ ((𝜑 → 𝜓) ∨ (𝜑 → ¬ 𝜓))

Proof of Theorem pm5.12

Step	Hyp	Ref	Expression
1		pm2.51 172	. 2 ⊢ (¬ (𝜑 → 𝜓) → (𝜑 → ¬ 𝜓))
2	1	orri 858	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 206  df-or 844

This theorem is referenced by: (None)