Theorem mt3d

Description: Modus tollens deduction. (Contributed by NM, 26-Mar-1995)

	Ref	Expression
Hypotheses	mt3d.1	$$⊢\phi \to \neg \chi$$
	mt3d.2	$$⊢\phi \to \left(\neg \psi \to \chi \right)$$
Assertion	mt3d	$$⊢\phi \to \psi$$

Proof

Step	Hyp	Ref	Expression
1		mt3d.1	$$⊢\phi \to \neg \chi$$
2		mt3d.2	$$⊢\phi \to \left(\neg \psi \to \chi \right)$$
3	2	con1d	$$⊢\phi \to \left(\neg \chi \to \psi \right)$$
4	1 3	mpd	$$⊢\phi \to \psi$$