Theorem jcndOLD

Description: Obsolete version of jcnd as of 10-Apr-2024. (Contributed by Glauco Siliprandi, 11-Dec-2019) (New usage is discouraged.) (Proof modification is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		jcndOLD.1	$$⊢\phi \to \psi$$
2		jcndOLD.2	$$⊢\phi \to \neg \chi$$
3	1 2	jc	$$⊢\phi \to \neg \left(\psi \to \neg \neg \chi \right)$$
4		notnotb	$$⊢\chi \leftrightarrow \neg \neg \chi$$
5	4	imbi2i	$$⊢\left(\psi \to \chi \right)\leftrightarrow \left(\psi \to \neg \neg \chi \right)$$
6	3 5	sylnibr	$$⊢\phi \to \neg \left(\psi \to \chi \right)$$