Theorem jcnd

Description: Deduction joining the consequents of two premises. (Contributed by Glauco Siliprandi, 11-Dec-2019) (Proof shortened by Wolf Lammen, 10-Apr-2024)

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

Proof

Step	Hyp	Ref	Expression
1		jcnd.1	$$⊢\phi \to \psi$$
2		jcnd.2	$$⊢\phi \to \neg \chi$$
3		jcn	$$⊢\psi \to \left(\neg \chi \to \neg \left(\psi \to \chi \right)\right)$$
4	1 2 3	sylc	$$⊢\phi \to \neg \left(\psi \to \chi \right)$$