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Metamath Proof Explorer

Theorem 3orel1

Description: Partial elimination of a triple disjunction by denial of a disjunct. (Contributed by Scott Fenton, 26-Mar-2011)

Ref Expression
Assertion 3orel1 ⊢ ¬ φ → φ ∨ ψ ∨ χ → ψ ∨ χ

Proof

Step Hyp Ref Expression
1 3orass ⊢ φ ∨ ψ ∨ χ ↔ φ ∨ ψ ∨ χ
2 orel1 ⊢ ¬ φ → φ ∨ ψ ∨ χ → ψ ∨ χ
3 1 2 biimtrid ⊢ ¬ φ → φ ∨ ψ ∨ χ → ψ ∨ χ