Theorem mt2bi

Description: A false consequent falsifies an antecedent. (Contributed by NM, 19-Aug-1993) (Proof shortened by Wolf Lammen, 12-Nov-2012)

	Ref	Expression
Hypothesis	mt2bi.1	$$⊢\phi$$
Assertion	mt2bi	$$⊢\neg \psi \leftrightarrow \left(\psi \to \neg \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		mt2bi.1	$$⊢\phi$$
2	1	a1bi	$$⊢\neg \psi \leftrightarrow \left(\phi \to \neg \psi \right)$$
3		con2b	$$⊢\left(\phi \to \neg \psi \right)\leftrightarrow \left(\psi \to \neg \phi \right)$$
4	2 3	bitri	$$⊢\neg \psi \leftrightarrow \left(\psi \to \neg \phi \right)$$