Theorem mt4d

Description: Modus tollens deduction. Deduction form of mt4 . (Contributed by NM, 9-Jun-2006)

	Ref	Expression
Hypotheses	mt4d.1	$$⊢\phi \to \psi$$
	mt4d.2	$$⊢\phi \to \left(\neg \chi \to \neg \psi \right)$$
Assertion	mt4d	$$⊢\phi \to \chi$$

Proof

Step	Hyp	Ref	Expression
1		mt4d.1	$$⊢\phi \to \psi$$
2		mt4d.2	$$⊢\phi \to \left(\neg \chi \to \neg \psi \right)$$
3	2	con4d	$$⊢\phi \to \left(\psi \to \chi \right)$$
4	1 3	mpd	$$⊢\phi \to \chi$$