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Theorem oran 1017
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 1016 . 2 ((¬ 𝜑 ∧ ¬ 𝜓) ↔ ¬ (𝜑𝜓))
21con2bii 349 1 ((𝜑𝜓) ↔ ¬ (¬ 𝜑 ∧ ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 198  wa 386  wo 878
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 199  df-an 387  df-or 879
This theorem is referenced by:  pm4.57  1018  19.43OLD  1986  ordthauslem  21558  mideulem2  26043  opphllem  26044  ordtconnlem1  30504  poimirlem9  33955  ftc1anclem1  34021  xrlttri5d  40287
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