Theorem con1b

Description: Contraposition. Bidirectional version of con1 . (Contributed by NM, 3-Jan-1993)

	Ref	Expression
Assertion	con1b	$$⊢\left(\neg \phi \to \psi \right)\leftrightarrow \left(\neg \psi \to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		con1	$$⊢\left(\neg \phi \to \psi \right)\to \left(\neg \psi \to \phi \right)$$
2		con1	$$⊢\left(\neg \psi \to \phi \right)\to \left(\neg \phi \to \psi \right)$$
3	1 2	impbii	$$⊢\left(\neg \phi \to \psi \right)\leftrightarrow \left(\neg \psi \to \phi \right)$$