Theorem pm2.65d

Description: Deduction for proof by contradiction. (Contributed by NM, 26-Jun-1994) (Proof shortened by Wolf Lammen, 26-May-2013)

	Ref	Expression
Hypotheses	pm2.65d.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
	pm2.65d.2	$$⊢\phi \to \left(\psi \to \neg \chi \right)$$
Assertion	pm2.65d	$$⊢\phi \to \neg \psi$$

Proof

Step	Hyp	Ref	Expression
1		pm2.65d.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		pm2.65d.2	$$⊢\phi \to \left(\psi \to \neg \chi \right)$$
3	2 1	nsyld	$$⊢\phi \to \left(\psi \to \neg \psi \right)$$
4	3	pm2.01d	$$⊢\phi \to \neg \psi$$