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Theorem 3ianor 949
Description: Negated triple conjunction expressed in terms of triple disjunction. (Contributed by Jeff Hankins, 15-Aug-2009.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Assertion
Ref Expression
3ianor  |-  ( -.  ( ph  /\  ps  /\ 
ch )  <->  ( -.  ph  \/  -.  ps  \/  -.  ch ) )

Proof of Theorem 3ianor
StepHypRef Expression
1 3anor 948 . . 3  |-  ( (
ph  /\  ps  /\  ch ) 
<->  -.  ( -.  ph  \/  -.  ps  \/  -.  ch ) )
21con2bii 322 . 2  |-  ( ( -.  ph  \/  -.  ps  \/  -.  ch )  <->  -.  ( ph  /\  ps  /\ 
ch ) )
32bicomi 193 1  |-  ( -.  ( ph  /\  ps  /\ 
ch )  <->  ( -.  ph  \/  -.  ps  \/  -.  ch ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    \/ w3o 933    /\ w3a 934
This theorem is referenced by:  fr3nr  4587  lpni  20862  xrdifh  23288  itg2addnclem  25003  dvreasin  25026  gltpntl  26175  pdiveql  26271  elfznelfzo  28213  hashtpg  28217  nbusgra  28277  trlonprop  28341  spthispth  28359
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  df-3or 935  df-3an 936
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