Theorem imnan

Description: Express an implication in terms of a negated conjunction. (Contributed by NM, 9-Apr-1994)

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

Proof

Step	Hyp	Ref	Expression
1		df-an	$$⊢\left(\phi \wedge \psi \right)\leftrightarrow \neg \left(\phi \to \neg \psi \right)$$
2	1	con2bii	$$⊢\left(\phi \to \neg \psi \right)\leftrightarrow \neg \left(\phi \wedge \psi \right)$$