Theorem pm2.8 988

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		pm2.53 865	. . 3 ⊢ ((𝜑 ∨ 𝜓) → (¬ 𝜑 → 𝜓))
2	1	con1d 146	. 2 ⊢ ((𝜑 ∨ 𝜓) → (¬ 𝜓 → 𝜑))
3	2	orim1d 981	1 ⊢ ((𝜑 ∨ 𝜓) → ((¬ 𝜓 ∨ 𝜒) → (𝜑 ∨ 𝜒)))

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-an 402  df-or 862

This theorem is used by: (None)