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Theorem pm2.26dc 902
Description: Decidable proposition version of theorem *2.26 of [WhiteheadRussell] p. 104. (Contributed by Jim Kingdon, 20-Apr-2018.)
Assertion
Ref Expression
pm2.26dc  |-  (DECID  ph  ->  ( -.  ph  \/  (
( ph  ->  ps )  ->  ps ) ) )

Proof of Theorem pm2.26dc
StepHypRef Expression
1 pm2.27 40 . 2  |-  ( ph  ->  ( ( ph  ->  ps )  ->  ps )
)
2 imordc 892 . 2  |-  (DECID  ph  ->  ( ( ph  ->  (
( ph  ->  ps )  ->  ps ) )  <->  ( -.  ph  \/  ( ( ph  ->  ps )  ->  ps ) ) ) )
31, 2mpbii 147 1  |-  (DECID  ph  ->  ( -.  ph  \/  (
( ph  ->  ps )  ->  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 703  DECID wdc 829
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 609  ax-in2 610  ax-io 704
This theorem depends on definitions:  df-bi 116  df-dc 830
This theorem is referenced by: (None)
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