Theorem nsyl

Description: A negated syllogism inference. (Contributed by NM, 31-Dec-1993) (Proof shortened by Wolf Lammen, 2-Mar-2013)

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

Proof

Step	Hyp	Ref	Expression
1		nsyl.1	$$⊢\phi \to \neg \psi$$
2		nsyl.2	$$⊢\chi \to \psi$$
3	1 2	nsyl3	$$⊢\chi \to \neg \phi$$
4	3	con2i	$$⊢\phi \to \neg \chi$$