Theorem nannot

Description: Negation in terms of alternative denial. (Contributed by Jeff Hoffman, 19-Nov-2007) (Revised by Wolf Lammen, 26-Jun-2020)

	Ref	Expression
Assertion	nannot	$$⊢\neg \phi \leftrightarrow \left(\phi ⊼\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		dfnan2	$$⊢\left(\phi ⊼\phi \right)\leftrightarrow \left(\phi \to \neg \phi \right)$$
2		pm4.8	$$⊢\left(\phi \to \neg \phi \right)\leftrightarrow \neg \phi$$
3	1 2	bitr2i	$$⊢\neg \phi \leftrightarrow \left(\phi ⊼\phi \right)$$