Theorem con5

Description: Biconditional contraposition variation. This proof is con5VD automatically translated and minimized. (Contributed by Alan Sare, 21-Apr-2013) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	con5	$$⊢\left(\phi \leftrightarrow \neg \psi \right)\to \left(\neg \phi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		biimpr	$$⊢\left(\phi \leftrightarrow \neg \psi \right)\to \left(\neg \psi \to \phi \right)$$
2	1	con1d	$$⊢\left(\phi \leftrightarrow \neg \psi \right)\to \left(\neg \phi \to \psi \right)$$