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	⊢ ( ¬ ( 𝜑 ∨ 𝜓 ) → ( 𝜑 ↔ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		orc	⊢ ( 𝜑 → ( 𝜑 ∨ 𝜓 ) )
2		olc	⊢ ( 𝜓 → ( 𝜑 ∨ 𝜓 ) )
3	1 2	pm5.21ni	⊢ ( ¬ ( 𝜑 ∨ 𝜓 ) → ( 𝜑 ↔ 𝜓 ) )