Metamath Proof Explorer


Theorem pm2.61nii

Description: Inference eliminating two antecedents. (Contributed by NM, 13-Jul-2005) (Proof shortened by Andrew Salmon, 25-May-2011) (Proof shortened by Wolf Lammen, 13-Nov-2012)

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

Proof

Step Hyp Ref Expression
1 pm2.61nii.1 ⊢ φ → ψ → χ
2 pm2.61nii.2 ⊢ ¬ φ → χ
3 pm2.61nii.3 ⊢ ¬ ψ → χ
4 1 3 pm2.61d1 ⊢ φ → χ
5 4 2 pm2.61i ⊢ χ