Theorem con34b

Description: A biconditional form of contraposition. Theorem *4.1 of WhiteheadRussell p. 116. (Contributed by NM, 11-May-1993)

	Ref	Expression
Assertion	con34b	$$⊢\left(\phi \to \psi \right)\leftrightarrow \left(\neg \psi \to \neg \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		con3	$$⊢\left(\phi \to \psi \right)\to \left(\neg \psi \to \neg \phi \right)$$
2		con4	$$⊢\left(\neg \psi \to \neg \phi \right)\to \left(\phi \to \psi \right)$$
3	1 2	impbii	$$⊢\left(\phi \to \psi \right)\leftrightarrow \left(\neg \psi \to \neg \phi \right)$$