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	⊢ ( 𝜑 → 𝜓 )
	jcndOLD.2	⊢ ( 𝜑 → ¬ 𝜒 )
Assertion	jcndOLD	⊢ ( 𝜑 → ¬ ( 𝜓 → 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		jcndOLD.1	⊢ ( 𝜑 → 𝜓 )
2		jcndOLD.2	⊢ ( 𝜑 → ¬ 𝜒 )
3	1 2	jc	⊢ ( 𝜑 → ¬ ( 𝜓 → ¬ ¬ 𝜒 ) )
4		notnotb	⊢ ( 𝜒 ↔ ¬ ¬ 𝜒 )
5	4	imbi2i	⊢ ( ( 𝜓 → 𝜒 ) ↔ ( 𝜓 → ¬ ¬ 𝜒 ) )
6	3 5	sylnibr	⊢ ( 𝜑 → ¬ ( 𝜓 → 𝜒 ) )