Theorem jcn

Description: Theorem joining the consequents of two premises. Theorem 8 of Margaris p. 60. (Contributed by NM, 5-Aug-1993) (Proof shortened by Josh Purinton, 29-Dec-2000)

	Ref	Expression
Assertion	jcn	$$⊢\phi \to \left(\neg \psi \to \neg \left(\phi \to \psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		pm2.27	$$⊢\phi \to \left(\left(\phi \to \psi \right)\to \psi \right)$$
2	1	con3d	$$⊢\phi \to \left(\neg \psi \to \neg \left(\phi \to \psi \right)\right)$$