Theorem pm2.8 970

Description: Theorem *2.8 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 5-Jan-2013.)

Assertion

Ref	Expression
pm2.8	⊢ ((𝜑 ∨ 𝜓) → ((¬ 𝜓 ∨ 𝜒) → (𝜑 ∨ 𝜒)))

Proof of Theorem pm2.8

Step	Hyp	Ref	Expression
1		pm2.53 848	. . 3 ⊢ ((𝜑 ∨ 𝜓) → (¬ 𝜑 → 𝜓))
2	1	con1d 145	. 2 ⊢ ((𝜑 ∨ 𝜓) → (¬ 𝜓 → 𝜑))
3	2	orim1d 963	1 ⊢ ((𝜑 ∨ 𝜓) → ((¬ 𝜓 ∨ 𝜒) → (𝜑 ∨ 𝜒)))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 844

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-an 397  df-or 845

This theorem is referenced by: (None)