Metamath Proof Explorer


Theorem pm2.01da

Description: Deduction based on reductio ad absurdum. See pm2.01 . (Contributed by Mario Carneiro, 9-Feb-2017)

Ref Expression
Hypothesis pm2.01da.1 ⊢ φ ∧ ψ → ¬ ψ
Assertion pm2.01da ⊢ φ → ¬ ψ

Proof

Step Hyp Ref Expression
1 pm2.01da.1 ⊢ φ ∧ ψ → ¬ ψ
2 1 ex ⊢ φ → ψ → ¬ ψ
3 2 pm2.01d ⊢ φ → ¬ ψ