Theorem noror

Description: \/ is expressible via -\/ . (Contributed by Remi, 26-Oct-2023) (Proof shortened by Wolf Lammen, 8-Dec-2023)

	Ref	Expression
Assertion	noror	$$⊢\left(\phi \vee \psi \right)\leftrightarrow \left(\left(\phi ⊽\psi \right)⊽\left(\phi ⊽\psi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		df-nor	$$⊢\left(\phi ⊽\psi \right)\leftrightarrow \neg \left(\phi \vee \psi \right)$$
2	1	con2bii	$$⊢\left(\phi \vee \psi \right)\leftrightarrow \neg \left(\phi ⊽\psi \right)$$
3		nornot	$$⊢\neg \left(\phi ⊽\psi \right)\leftrightarrow \left(\left(\phi ⊽\psi \right)⊽\left(\phi ⊽\psi \right)\right)$$
4	2 3	bitri	$$⊢\left(\phi \vee \psi \right)\leftrightarrow \left(\left(\phi ⊽\psi \right)⊽\left(\phi ⊽\psi \right)\right)$$