Theorem mt2i

Description: Modus tollens inference. (Contributed by NM, 26-Mar-1995) (Proof shortened by Wolf Lammen, 15-Sep-2012)

	Ref	Expression
Hypotheses	mt2i.1	$$⊢\chi$$
	mt2i.2	$$⊢\phi \to \left(\psi \to \neg \chi \right)$$
Assertion	mt2i	$$⊢\phi \to \neg \psi$$

Proof

Step	Hyp	Ref	Expression
1		mt2i.1	$$⊢\chi$$
2		mt2i.2	$$⊢\phi \to \left(\psi \to \neg \chi \right)$$
3	1	a1i	$$⊢\phi \to \chi$$
4	3 2	mt2d	$$⊢\phi \to \neg \psi$$