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

Proof

Step	Hyp	Ref	Expression
1		jcnd.1	⊢ ( 𝜑 → 𝜓 )
2		jcnd.2	⊢ ( 𝜑 → ¬ 𝜒 )
3		jcn	⊢ ( 𝜓 → ( ¬ 𝜒 → ¬ ( 𝜓 → 𝜒 ) ) )
4	1 2 3	sylc	⊢ ( 𝜑 → ¬ ( 𝜓 → 𝜒 ) )