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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