Theorem mt2

Description: A rule similar to modus tollens. Inference associated with con2i . (Contributed by NM, 19-Aug-1993) (Proof shortened by Wolf Lammen, 10-Sep-2013)

	Ref	Expression
Hypotheses	mt2.1	$$⊢\psi$$
	mt2.2	$$⊢\phi \to \neg \psi$$
Assertion	mt2	$$⊢\neg \phi$$

Proof

Step	Hyp	Ref	Expression
1		mt2.1	$$⊢\psi$$
2		mt2.2	$$⊢\phi \to \neg \psi$$
3	1	a1i	$$⊢\phi \to \psi$$
4	3 2	pm2.65i	$$⊢\neg \phi$$