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Theorem oran 482
Description: Disjunction in terms of conjunction (DeMorgan's law). Compare Theorem *4.57 of [WhiteheadRussell] p. 120. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 7-May-2011.)
Assertion
Ref Expression
oran  |-  ( (
ph  \/  ps )  <->  -.  ( -.  ph  /\  -.  ps ) )

Proof of Theorem oran
StepHypRef Expression
1 pm4.56 481 . 2  |-  ( ( -.  ph  /\  -.  ps ) 
<->  -.  ( ph  \/  ps ) )
21con2bii 322 1  |-  ( (
ph  \/  ps )  <->  -.  ( -.  ph  /\  -.  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    \/ wo 357    /\ wa 358
This theorem is referenced by:  pm4.57  483  19.43OLD  1593  ordthauslem  17111
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360
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