Theorem nsyl2

Description: A negated syllogism inference. (Contributed by NM, 26-Jun-1994) (Proof shortened by Wolf Lammen, 14-Nov-2023)

	Ref	Expression
Hypotheses	nsyl2.1	$$⊢\phi \to \neg \psi$$
	nsyl2.2	$$⊢\neg \chi \to \psi$$
Assertion	nsyl2	$$⊢\phi \to \chi$$

Proof

Step	Hyp	Ref	Expression
1		nsyl2.1	$$⊢\phi \to \neg \psi$$
2		nsyl2.2	$$⊢\neg \chi \to \psi$$
3	1 2	nsyl3	$$⊢\neg \chi \to \neg \phi$$
4	3	con4i	$$⊢\phi \to \chi$$