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Theorem simprimdc 859
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 858 1  |-  (DECID  ps  ->  ( -.  ( ph  ->  -. 
ps )  ->  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4  DECID wdc 834
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-io 709
This theorem depends on definitions:  df-bi 117  df-stab 831  df-dc 835
This theorem is referenced by:  dfandc  884
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