Theorem nsyld

Description: A negated syllogism deduction. (Contributed by NM, 9-Apr-2005)

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

Proof

Step	Hyp	Ref	Expression
1		nsyld.1	$$⊢\phi \to \left(\psi \to \neg \chi \right)$$
2		nsyld.2	$$⊢\phi \to \left(\tau \to \chi \right)$$
3	2	con3d	$$⊢\phi \to \left(\neg \chi \to \neg \tau \right)$$
4	1 3	syld	$$⊢\phi \to \left(\psi \to \neg \tau \right)$$