Theorem oran 986

Description: Disjunction in terms of conjunction (De Morgan's law). Compare Theorem *4.57 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-1993.) (Proof shortened by Andrew Salmon, 7-May-2011.)

Assertion

Ref	Expression
oran	⊢ ((𝜑 ∨ 𝜓) ↔ ¬ (¬ 𝜑 ∧ ¬ 𝜓))

Proof of Theorem oran

Step	Hyp	Ref	Expression
1		pm4.56 985	. 2 ⊢ ((¬ 𝜑 ∧ ¬ 𝜓) ↔ ¬ (𝜑 ∨ 𝜓))
2	1	con2bii 357	1 ⊢ ((𝜑 ∨ 𝜓) ↔ ¬ (¬ 𝜑 ∧ ¬ 𝜓))

Syntax hints:  ¬ wn 3   ↔ wb 205   ∧ wa 395   ∨ 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-an 396  df-or 845

This theorem is referenced by:  pm4.57  987  19.43OLD  1878  ordthauslem  23211  mideulem2  28457  opphllem  28458  ordtconnlem1  33396  poimirlem9  36991  ftc1anclem1  37055  onsucf1olem  42534  xrlttri5d  44503