Theorem nanan

Description: Conjunction in terms of alternative denial. (Contributed by Mario Carneiro, 9-May-2015)

	Ref	Expression
Assertion	nanan	$$⊢\left(\phi \wedge \psi \right)\leftrightarrow \neg \left(\phi ⊼\psi \right)$$

Proof

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