Theorem nsyl4

Description: A negated syllogism inference. (Contributed by NM, 15-Feb-1996)

	Ref	Expression
Hypotheses	nsyl4.1	$$⊢\phi \to \psi$$
	nsyl4.2	$$⊢\neg \phi \to \chi$$
Assertion	nsyl4	$$⊢\neg \chi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		nsyl4.1	$$⊢\phi \to \psi$$
2		nsyl4.2	$$⊢\neg \phi \to \chi$$
3	2	con1i	$$⊢\neg \chi \to \phi$$
4	3 1	syl	$$⊢\neg \chi \to \psi$$