Theorem con2b

Description: Contraposition. Bidirectional version of con2 . (Contributed by NM, 12-Mar-1993)

	Ref	Expression
Assertion	con2b	$$⊢\left(\phi \to \neg \psi \right)\leftrightarrow \left(\psi \to \neg \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		con2	$$⊢\left(\phi \to \neg \psi \right)\to \left(\psi \to \neg \phi \right)$$
2		con2	$$⊢\left(\psi \to \neg \phi \right)\to \left(\phi \to \neg \psi \right)$$
3	1 2	impbii	$$⊢\left(\phi \to \neg \psi \right)\leftrightarrow \left(\psi \to \neg \phi \right)$$