Theorem biorfri

Description: A wff is equivalent to its disjunction with falsehood. (Contributed by NM, 23-Mar-1995) (Proof shortened by Wolf Lammen, 16-Jul-2021) (Proof shortened by AV, 10-Aug-2025)

	Ref	Expression
Hypothesis	biorfi.1	$$⊢\neg \phi$$
Assertion	biorfri	$$⊢\psi \leftrightarrow \left(\psi \vee \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		biorfi.1	$$⊢\neg \phi$$
2	1	biorfi	$$⊢\psi \leftrightarrow \left(\phi \vee \psi \right)$$
3		orcom	$$⊢\left(\phi \vee \psi \right)\leftrightarrow \left(\psi \vee \phi \right)$$
4	2 3	bitri	$$⊢\psi \leftrightarrow \left(\psi \vee \phi \right)$$