Theorem mt4i

Description: Modus tollens inference. (Contributed by Wolf Lammen, 12-May-2013)

	Ref	Expression
Hypotheses	mt4i.1	$$⊢\chi$$
	mt4i.2	$$⊢\phi \to \left(\neg \psi \to \neg \chi \right)$$
Assertion	mt4i	$$⊢\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		mt4i.1	$$⊢\chi$$
2		mt4i.2	$$⊢\phi \to \left(\neg \psi \to \neg \chi \right)$$
3	1	a1i	$$⊢\phi \to \chi$$
4	3 2	mt4d	$$⊢\phi \to \psi$$