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Theorem 3bior1fd 1324
Description: A disjunction is equivalent to a threefold disjunction with single falsehood, analogous to biorf 405. (Contributed by Alexander van der Vekens, 8-Sep-2017.)
Hypothesis
Ref Expression
3biorfd.1  |-  ( ph  ->  -.  th )
Assertion
Ref Expression
3bior1fd  |-  ( ph  ->  ( ( ch  \/  ps )  <->  ( th  \/  ch  \/  ps ) ) )

Proof of Theorem 3bior1fd
StepHypRef Expression
1 3biorfd.1 . . 3  |-  ( ph  ->  -.  th )
2 biorf 405 . . 3  |-  ( -. 
th  ->  ( ( ch  \/  ps )  <->  ( th  \/  ( ch  \/  ps ) ) ) )
31, 2syl 16 . 2  |-  ( ph  ->  ( ( ch  \/  ps )  <->  ( th  \/  ( ch  \/  ps ) ) ) )
4 3orass 968 . 2  |-  ( ( th  \/  ch  \/  ps )  <->  ( th  \/  ( ch  \/  ps ) ) )
53, 4syl6bbr 263 1  |-  ( ph  ->  ( ( ch  \/  ps )  <->  ( th  \/  ch  \/  ps ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 184    \/ wo 368    \/ w3o 964
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-or 370  df-3or 966
This theorem is referenced by:  3bior1fand  1325  3bior2fd  1326  nb3graprlem2  23359
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