This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem pm2.65d

Description: Deduction for proof by contradiction. (Contributed by NM, 26-Jun-1994) (Proof shortened by Wolf Lammen, 26-May-2013)

Ref Expression
Hypotheses pm2.65d.1 ⊢ φ → ψ → χ
pm2.65d.2 ⊢ φ → ψ → ¬ χ
Assertion pm2.65d ⊢ φ → ¬ ψ

Proof

Step Hyp Ref Expression
1 pm2.65d.1 ⊢ φ → ψ → χ
2 pm2.65d.2 ⊢ φ → ψ → ¬ χ
3 2 1 nsyld ⊢ φ → ψ → ¬ ψ
4 3 pm2.01d ⊢ φ → ¬ ψ