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Theorem oran 974
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 pm4.56 973 . 2 ((¬ 𝜑 ∧ ¬ 𝜓) ↔ ¬ (𝜑𝜓))
21con2bii 346 1 ((𝜑𝜓) ↔ ¬ (¬ 𝜑 ∧ ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wa 382  wo 836
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-an 383  df-or 837
This theorem is referenced by:  pm4.57  975  19.43OLD  1963  ordthauslem  21408  mideulem2  25847  opphllem  25848  ordtconnlem1  30310  poimirlem9  33751  ftc1anclem1  33817  xrlttri5d  40010
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