Theorem pm2.01d 608

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		pm2.01 606	. 2 ⊢ ((𝜓 → ¬ 𝜓) → ¬ 𝜓)
3	1, 2	syl 14	1 ⊢ (𝜑 → ¬ 𝜓)

Syntax hints:  ¬ wn 3   → wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 604

This theorem is referenced by:  pm2.01da  626  pm2.65d  650  pm5.19  696  mtord  773  swopo  4284  rennim  10944  absle  11031  bj-nnclavius  13618