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Theorem ts3or2 33961
Description: A Tseitin axiom for triple logical disjunction, in deduction form. (Contributed by Giovanni Mascellani, 25-Mar-2018.)
Assertion
Ref Expression
ts3or2  |-  ( th 
->  ( -.  ( ph  \/  ps )  \/  ( ph  \/  ps  \/  ch ) ) )

Proof of Theorem ts3or2
StepHypRef Expression
1 tsor2 33955 . 2  |-  ( th 
->  ( -.  ( ph  \/  ps )  \/  (
( ph  \/  ps )  \/  ch )
) )
2 df-3or 1038 . . 3  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ( ph  \/  ps )  \/  ch ) )
32orbi2i 541 . 2  |-  ( ( -.  ( ph  \/  ps )  \/  ( ph  \/  ps  \/  ch ) )  <->  ( -.  ( ph  \/  ps )  \/  ( ( ph  \/  ps )  \/  ch ) ) )
41, 3sylibr 224 1  |-  ( th 
->  ( -.  ( ph  \/  ps )  \/  ( ph  \/  ps  \/  ch ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 383    \/ w3o 1036
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 197  df-or 385  df-3or 1038
This theorem is referenced by: (None)
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