Theorem nsyl5

Description: A negated syllogism inference. (Contributed by Wolf Lammen, 20-May-2024)

	Ref	Expression
Hypotheses	nsyl4.1	$$⊢\phi \to \psi$$
	nsyl4.2	$$⊢\neg \phi \to \chi$$
Assertion	nsyl5	$$⊢\neg \psi \to \chi$$

Proof

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