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Metamath Proof Explorer

Theorem pm2.61ii

Description: Inference eliminating two antecedents. (Contributed by NM, 4-Jan-1993) (Proof shortened by Josh Purinton, 29-Dec-2000)

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

Proof

Step Hyp Ref Expression
1 pm2.61ii.1 ⊢ ¬ φ → ¬ ψ → χ
2 pm2.61ii.2 ⊢ φ → χ
3 pm2.61ii.3 ⊢ ψ → χ
4 1 3 pm2.61d2 ⊢ ¬ φ → χ
5 2 4 pm2.61i ⊢ χ