Theorem pm2.01d 619

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		pm2.01 617	. 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 615

This theorem is referenced by:  pm2.01da  637  pm2.65d  661  pm5.19  707  mtord  784  swopo  4337  rennim  11146  absle  11233  bj-nnclavius  15229