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Theorem 3ioran 950
Description: Negated triple disjunction as triple conjunction. (Contributed by Scott Fenton, 19-Apr-2011.)
Assertion
Ref Expression
3ioran  |-  ( -.  ( ph  \/  ps  \/  ch )  <->  ( -.  ph 
/\  -.  ps  /\  -.  ch ) )

Proof of Theorem 3ioran
StepHypRef Expression
1 ioran 476 . . 3  |-  ( -.  ( ph  \/  ps ) 
<->  ( -.  ph  /\  -.  ps ) )
21anbi1i 676 . 2  |-  ( ( -.  ( ph  \/  ps )  /\  -.  ch ) 
<->  ( ( -.  ph  /\ 
-.  ps )  /\  -.  ch ) )
3 ioran 476 . . 3  |-  ( -.  ( ( ph  \/  ps )  \/  ch ) 
<->  ( -.  ( ph  \/  ps )  /\  -.  ch ) )
4 df-3or 935 . . 3  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ( ph  \/  ps )  \/  ch ) )
53, 4xchnxbir 300 . 2  |-  ( -.  ( ph  \/  ps  \/  ch )  <->  ( -.  ( ph  \/  ps )  /\  -.  ch ) )
6 df-3an 936 . 2  |-  ( ( -.  ph  /\  -.  ps  /\ 
-.  ch )  <->  ( ( -.  ph  /\  -.  ps )  /\  -.  ch )
)
72, 5, 63bitr4i 268 1  |-  ( -.  ( ph  \/  ps  \/  ch )  <->  ( -.  ph 
/\  -.  ps  /\  -.  ch ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    \/ wo 357    /\ wa 358    \/ w3o 933    /\ w3a 934
This theorem is referenced by:  3oran  951  cadnot  1384  fbunfip  17564  bsstrs  26146  nbssntrs  26147
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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