Theorem mtod

Description: Modus tollens deduction. (Contributed by NM, 3-Apr-1994) (Proof shortened by Wolf Lammen, 11-Sep-2013)

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

Proof

Step	Hyp	Ref	Expression
1		mtod.1	$$⊢\phi \to \neg \chi$$
2		mtod.2	$$⊢\phi \to \left(\psi \to \chi \right)$$
3	1	a1d	$$⊢\phi \to \left(\psi \to \neg \chi \right)$$
4	2 3	pm2.65d	$$⊢\phi \to \neg \psi$$