Theorem nornot

Description: -. is expressible via -\/ . (Contributed by Remi, 25-Oct-2023) (Proof shortened by Wolf Lammen, 8-Dec-2023)

	Ref	Expression
Assertion	nornot	$$⊢\neg \phi \leftrightarrow \left(\phi ⊽\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		df-nor	$$⊢\left(\phi ⊽\phi \right)\leftrightarrow \neg \left(\phi \vee \phi \right)$$
2		oridm	$$⊢\left(\phi \vee \phi \right)\leftrightarrow \phi$$
3	1 2	xchbinx	$$⊢\left(\phi ⊽\phi \right)\leftrightarrow \neg \phi$$
4	3	bicomi	$$⊢\neg \phi \leftrightarrow \left(\phi ⊽\phi \right)$$