Theorem pm5.14 926

Description: Theorem *5.14 of [WhiteheadRussell] p. 123. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm5.14	⊢ ((𝜑 → 𝜓) ∨ (𝜓 → 𝜒))

Proof of Theorem pm5.14

Step	Hyp	Ref	Expression
1		ax-1 6	. . . 4 ⊢ (𝜓 → (𝜑 → 𝜓))
2	1	con3i 149	. . 3 ⊢ (¬ (𝜑 → 𝜓) → ¬ 𝜓)
3	2	pm2.21d 117	. 2 ⊢ (¬ (𝜑 → 𝜓) → (𝜓 → 𝜒))
4	3	orri 390	1 ⊢ ((𝜑 → 𝜓) ∨ (𝜓 → 𝜒))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 382

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 196  df-or 384

This theorem is referenced by:  pm5.13  927