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Theorem oran 494
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  |-  ( (
ph  \/  ps )  <->  -.  ( -.  ph  /\  -.  ps ) )

Proof of Theorem oran
StepHypRef Expression
1 pm4.56 493 . 2  |-  ( ( -.  ph  /\  -.  ps ) 
<->  -.  ( ph  \/  ps ) )
21con2bii 330 1  |-  ( (
ph  \/  ps )  <->  -.  ( -.  ph  /\  -.  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184    \/ wo 366    /\ wa 367
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 185  df-or 368  df-an 369
This theorem is referenced by:  pm4.57  495  nbiorOLD  859  19.43OLD  1699  ordthauslem  20051  mideulem2  24309  opphllem  24310  ordtconlem1  28141  ftc1anclem1  30330  xrlttri5d  31705
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