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