Theorem jc

Description: Deduction joining the consequents of two premises. A deduction associated with pm3.2im . (Contributed by NM, 28-Dec-1992)

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

Proof

Step	Hyp	Ref	Expression
1		jc.1	$$⊢\phi \to \psi$$
2		jc.2	$$⊢\phi \to \chi$$
3		pm3.2im	$$⊢\psi \to \left(\chi \to \neg \left(\psi \to \neg \chi \right)\right)$$
4	1 2 3	sylc	$$⊢\phi \to \neg \left(\psi \to \neg \chi \right)$$