Theorem pm2.65

Description: Theorem *2.65 of WhiteheadRussell p. 107. Proof by contradiction. (Contributed by NM, 21-Jun-1993) (Proof shortened by Wolf Lammen, 8-Mar-2013)

	Ref	Expression
Assertion	pm2.65	$$⊢\left(\phi \to \psi \right)\to \left(\left(\phi \to \neg \psi \right)\to \neg \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		idd	$$⊢\left(\phi \to \psi \right)\to \left(\neg \phi \to \neg \phi \right)$$
2		con3	$$⊢\left(\phi \to \psi \right)\to \left(\neg \psi \to \neg \phi \right)$$
3	1 2	jad	$$⊢\left(\phi \to \psi \right)\to \left(\left(\phi \to \neg \psi \right)\to \neg \phi \right)$$