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

Metamath Proof Explorer

Theorem pm2.65da

Description: Deduction for proof by contradiction. (Contributed by NM, 12-Jun-2014)

Ref Expression
Hypotheses pm2.65da.1 ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
pm2.65da.2 ⊢ ( ( 𝜑 ∧ 𝜓 ) → ¬ 𝜒 )
Assertion pm2.65da ( 𝜑 → ¬ 𝜓 )

Proof

Step Hyp Ref Expression
1 pm2.65da.1 ⊢ ( ( 𝜑 ∧ 𝜓 ) → 𝜒 )
2 pm2.65da.2 ⊢ ( ( 𝜑 ∧ 𝜓 ) → ¬ 𝜒 )
3 1 ex ⊢ ( 𝜑 → ( 𝜓 → 𝜒 ) )
4 2 ex ⊢ ( 𝜑 → ( 𝜓 → ¬ 𝜒 ) )
5 3 4 pm2.65d ⊢ ( 𝜑 → ¬ 𝜓 )