Theorem norbi

Description: If neither of two propositions is true, then these propositions are equivalent. (Contributed by BJ, 26-Apr-2019)

	Ref	Expression
Assertion	norbi	$$⊢\neg \left(\phi \vee \psi \right)\to \left(\phi \leftrightarrow \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		orc	$$⊢\phi \to \left(\phi \vee \psi \right)$$
2		olc	$$⊢\psi \to \left(\phi \vee \psi \right)$$
3	1 2	pm5.21ni	$$⊢\neg \left(\phi \vee \psi \right)\to \left(\phi \leftrightarrow \psi \right)$$