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Metamath Proof Explorer

Theorem pm2.61iii

Description: Inference eliminating three antecedents. (Contributed by NM, 2-Jan-2002) (Proof shortened by Wolf Lammen, 22-Sep-2013)

Ref Expression
Hypotheses pm2.61iii.1 ⊢ ¬ φ → ¬ ψ → ¬ χ → θ
pm2.61iii.2 ⊢ φ → θ
pm2.61iii.3 ⊢ ψ → θ
pm2.61iii.4 ⊢ χ → θ
Assertion pm2.61iii ⊢ θ

Proof

Step Hyp Ref Expression
1 pm2.61iii.1 ⊢ ¬ φ → ¬ ψ → ¬ χ → θ
2 pm2.61iii.2 ⊢ φ → θ
3 pm2.61iii.3 ⊢ ψ → θ
4 pm2.61iii.4 ⊢ χ → θ
5 2 a1d ⊢ φ → ¬ χ → θ
6 3 a1d ⊢ ψ → ¬ χ → θ
7 1 5 6 pm2.61ii ⊢ ¬ χ → θ
8 4 7 pm2.61i ⊢ θ