Metamath Proof Explorer

Theorem pm2.8

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

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

Proof

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