Theorem pm2.01d 627

Description: Deduction based on reductio ad absurdum. (Contributed by NM, 18-Aug-1993.) (Revised by Mario Carneiro, 31-Jan-2015.)

Hypothesis

Ref	Expression
pm2.01d.1	⊢ (𝜑 → (𝜓 → ¬ 𝜓))

Assertion

Ref	Expression
pm2.01d	⊢ (𝜑 → ¬ 𝜓)

Proof of Theorem pm2.01d

Step	Hyp	Ref	Expression
1		pm2.01d.1	. 2 ⊢ (𝜑 → (𝜓 → ¬ 𝜓))
2		pm2.01 625	. 2 ⊢ ((𝜓 → ¬ 𝜓) → ¬ 𝜓)
3	1, 2	syl 14	1 ⊢ (𝜑 → ¬ 𝜓)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 623

This theorem is used by:  pm2.01da  645  pm2.65d  670  pm5.19  718  mtord  795  swopo  4451  rennim  11770  absle  11857  bj-nnclavius  16777