Theorem norbi 900

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 881	. 2 ⊢ (𝜑 → (𝜑 ∨ 𝜓))
2		olc 882	. 2 ⊢ (𝜓 → (𝜑 ∨ 𝜓))
3	1, 2	pm5.21ni 380	1 ⊢ (¬ (𝜑 ∨ 𝜓) → (𝜑 ↔ 𝜓))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ↔ wb 209   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  nbior  901  oibabs  966