Theorem mtoi

Description: Modus tollens inference. (Contributed by NM, 5-Jul-1994) (Proof shortened by Wolf Lammen, 15-Sep-2012)

	Ref	Expression
Hypotheses	mtoi.1	$$⊢\neg \chi$$
	mtoi.2	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	mtoi	$$⊢\phi \to \neg \psi$$

Proof

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