Theorem mt3i

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

	Ref	Expression
Hypotheses	mt3i.1	$$⊢\neg \chi$$
	mt3i.2	$$⊢\phi \to \left(\neg \psi \to \chi \right)$$
Assertion	mt3i	$$⊢\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		mt3i.1	$$⊢\neg \chi$$
2		mt3i.2	$$⊢\phi \to \left(\neg \psi \to \chi \right)$$
3	1	a1i	$$⊢\phi \to \neg \chi$$
4	3 2	mt3d	$$⊢\phi \to \psi$$