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Metamath Proof Explorer

Theorem pm2.61d

Description: Deduction eliminating an antecedent. (Contributed by NM, 27-Apr-1994) (Proof shortened by Wolf Lammen, 12-Sep-2013)

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

Proof

Step Hyp Ref Expression
1 pm2.61d.1 ⊢ φ → ψ → χ
2 pm2.61d.2 ⊢ φ → ¬ ψ → χ
3 2 con1d ⊢ φ → ¬ χ → ψ
4 3 1 syld ⊢ φ → ¬ χ → χ
5 4 pm2.18d ⊢ φ → χ