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Theorem oran 516
 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 ((𝜑𝜓) ↔ ¬ (¬ 𝜑 ∧ ¬ 𝜓))

Proof of Theorem oran
StepHypRef Expression
1 pm4.56 515 . 2 ((¬ 𝜑 ∧ ¬ 𝜓) ↔ ¬ (𝜑𝜓))
21con2bii 346 1 ((𝜑𝜓) ↔ ¬ (¬ 𝜑 ∧ ¬ 𝜓))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ↔ wb 196   ∨ wo 382   ∧ wa 383 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 197  df-or 384  df-an 385 This theorem is referenced by:  pm4.57  517  19.43OLD  1851  ordthauslem  21235  mideulem2  25671  opphllem  25672  ordtconnlem1  30098  poimirlem9  33548  ftc1anclem1  33615  xrlttri5d  39809
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