Theorem mt2d

Description: Modus tollens deduction. (Contributed by NM, 4-Jul-1994)

	Ref	Expression
Hypotheses	mt2d.1	$$⊢\phi \to \chi$$
	mt2d.2	$$⊢\phi \to \left(\psi \to \neg \chi \right)$$
Assertion	mt2d	$$⊢\phi \to \neg \psi$$

Proof

Step	Hyp	Ref	Expression
1		mt2d.1	$$⊢\phi \to \chi$$
2		mt2d.2	$$⊢\phi \to \left(\psi \to \neg \chi \right)$$
3	2	con2d	$$⊢\phi \to \left(\chi \to \neg \psi \right)$$
4	1 3	mpd	$$⊢\phi \to \neg \psi$$