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Theorem 3ianor 951
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 950 . . 3  |-  ( (
ph  /\  ps  /\  ch ) 
<->  -.  ( -.  ph  \/  -.  ps  \/  -.  ch ) )
21con2bii 323 . 2  |-  ( ( -.  ph  \/  -.  ps  \/  -.  ch )  <->  -.  ( ph  /\  ps  /\ 
ch ) )
32bicomi 194 1  |-  ( -.  ( ph  /\  ps  /\ 
ch )  <->  ( -.  ph  \/  -.  ps  \/  -.  ch ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 177    \/ w3o 935    /\ w3a 936
This theorem is referenced by:  tppreqb  3884  fr3nr  4702  funtpg  5443  bropopvvv  6367  elfznelfzo  11121  hashtpg  11620  nbusgra  21308  spthispth  21429  lpni  21617  xrdifh  23981  itg2addnclem  25959  dvreasin  25982
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 178  df-or 360  df-an 361  df-3or 937  df-3an 938
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