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Theorem simprimdc 790
Description: Simplification given a decidable proposition. Similar to Theorem *3.27 (Simp) of [WhiteheadRussell] p. 112. (Contributed by Jim Kingdon, 30-Apr-2018.)
Assertion
Ref Expression
simprimdc  |-  (DECID  ps  ->  ( -.  ( ph  ->  -. 
ps )  ->  ps ) )

Proof of Theorem simprimdc
StepHypRef Expression
1 idd 21 . . 3  |-  ( ph  ->  ( ps  ->  ps ) )
21a1i 9 . 2  |-  (DECID  ps  ->  (
ph  ->  ( ps  ->  ps ) ) )
32impidc 789 1  |-  (DECID  ps  ->  ( -.  ( ph  ->  -. 
ps )  ->  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4  DECID wdc 776
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663
This theorem depends on definitions:  df-bi 115  df-dc 777
This theorem is referenced by:  dfandc  812
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