Theorem pm2.01d 161

Description: Deduction based on reductio ad absurdum. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Wolf Lammen, 5-Mar-2013.)

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		id 19	. 2 ⊢ (¬ ψ → ¬ ψ)
3	1, 2	pm2.61d1 151	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-3 8

This theorem is referenced by:  pm2.65d  166  pm2.01da  429