Theorem norcomOLD

Description: Obsolete version of norcom as of 23-Apr-2024. (Contributed by Remi, 25-Oct-2023) (Proof modification is discouraged.) (New usage is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		orcom	$$⊢\left(\phi \vee \psi \right)\leftrightarrow \left(\psi \vee \phi \right)$$
2	1	notbii	$$⊢\neg \left(\phi \vee \psi \right)\leftrightarrow \neg \left(\psi \vee \phi \right)$$
3		df-nor	$$⊢\left(\phi ⊽\psi \right)\leftrightarrow \neg \left(\phi \vee \psi \right)$$
4		df-nor	$$⊢\left(\psi ⊽\phi \right)\leftrightarrow \neg \left(\psi \vee \phi \right)$$
5	2 3 4	3bitr4i	$$⊢\left(\phi ⊽\psi \right)\leftrightarrow \left(\psi ⊽\phi \right)$$