Theorem pm2.01d

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

	Ref	Expression
Hypothesis	pm2.01d.1	$$⊢\phi \to \left(\psi \to \neg \psi \right)$$
Assertion	pm2.01d	$$⊢\phi \to \neg \psi$$

Proof

Step	Hyp	Ref	Expression
1		pm2.01d.1	$$⊢\phi \to \left(\psi \to \neg \psi \right)$$
2		id	$$⊢\neg \psi \to \neg \psi$$
3	1 2	pm2.61d1	$$⊢\phi \to \neg \psi$$