Theorem norbi 884

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

Assertion

Ref	Expression
norbi	⊢ (¬ (𝜑 ∨ 𝜓) → (𝜑 ↔ 𝜓))

Proof of Theorem norbi

Step	Hyp	Ref	Expression
1		orc 864	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
2		olc 865	. 2 ⊢ (𝜓 → (𝜑 ∨ 𝜓))
3	1, 2	pm5.21ni 379	1 ⊢ (¬ (𝜑 ∨ 𝜓) → (𝜑 ↔ 𝜓))

Syntax hints:  ¬ wn 3   → wi 4   ↔ wb 205   ∨ wo 844

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-or 845

This theorem is referenced by:  nbior  885  oibabs  949