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Theorem oran 988
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 pm4.56 987 . 2 ((¬ 𝜑 ∧ ¬ 𝜓) ↔ ¬ (𝜑𝜓))
21con2bii 357 1 ((𝜑𝜓) ↔ ¬ (¬ 𝜑 ∧ ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 205  wa 396  wo 845
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 397  df-or 846
This theorem is referenced by:  pm4.57  989  19.43OLD  1886  ordthauslem  22878  mideulem2  27974  opphllem  27975  ordtconnlem1  32892  poimirlem9  36485  ftc1anclem1  36549  onsucf1olem  42005  xrlttri5d  43979
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