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Theorem pm2.25dc 863
Description: Elimination of disjunction based on a disjunction, for a decidable proposition. Based on theorem *2.25 of [WhiteheadRussell] p. 104. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm2.25dc  |-  (DECID  ph  ->  (
ph  \/  ( ( ph  \/  ps )  ->  ps ) ) )

Proof of Theorem pm2.25dc
StepHypRef Expression
1 df-dc 805 . 2  |-  (DECID  ph  <->  ( ph  \/  -.  ph ) )
2 orel1 699 . . 3  |-  ( -. 
ph  ->  ( ( ph  \/  ps )  ->  ps ) )
32orim2i 735 . 2  |-  ( (
ph  \/  -.  ph )  ->  ( ph  \/  (
( ph  \/  ps )  ->  ps ) ) )
41, 3sylbi 120 1  |-  (DECID  ph  ->  (
ph  \/  ( ( ph  \/  ps )  ->  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 682  DECID wdc 804
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-in2 589  ax-io 683
This theorem depends on definitions:  df-bi 116  df-dc 805
This theorem is referenced by: (None)
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