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Metamath Proof Explorer

Theorem pm2.82

Description: Theorem *2.82 of WhiteheadRussell p. 108. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion pm2.82 ⊢ φ ∨ ψ ∨ χ → φ ∨ ¬ χ ∨ θ → φ ∨ ψ ∨ θ

Proof

Step Hyp Ref Expression
1 pm2.24 ⊢ χ → ¬ χ → ψ
2 1 orim2d ⊢ χ → φ ∨ ¬ χ → φ ∨ ψ
3 2 jao1i ⊢ φ ∨ ψ ∨ χ → φ ∨ ¬ χ → φ ∨ ψ
4 3 orim1d ⊢ φ ∨ ψ ∨ χ → φ ∨ ¬ χ ∨ θ → φ ∨ ψ ∨ θ