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Theorem 3oran 951
Description: Triple disjunction in terms of triple conjunction. (Contributed by NM, 8-Oct-2012.)
Assertion
Ref Expression
3oran  |-  ( (
ph  \/  ps  \/  ch )  <->  -.  ( -.  ph 
/\  -.  ps  /\  -.  ch ) )

Proof of Theorem 3oran
StepHypRef Expression
1 3ioran 950 . . 3  |-  ( -.  ( ph  \/  ps  \/  ch )  <->  ( -.  ph 
/\  -.  ps  /\  -.  ch ) )
21con1bii 321 . 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:  dalawlem10  30691
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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