Theorem nsyl3

Description: A negated syllogism inference. (Contributed by NM, 1-Dec-1995)

	Ref	Expression
Hypotheses	nsyl3.1	$$⊢\phi \to \neg \psi$$
	nsyl3.2	$$⊢\chi \to \psi$$
Assertion	nsyl3	$$⊢\chi \to \neg \phi$$

Proof

Step	Hyp	Ref	Expression
1		nsyl3.1	$$⊢\phi \to \neg \psi$$
2		nsyl3.2	$$⊢\chi \to \psi$$
3	1	a1i	$$⊢\chi \to \left(\phi \to \neg \psi \right)$$
4	2 3	mt2d	$$⊢\chi \to \neg \phi$$