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Theorem simplimdc 846
Description: Simplification for a decidable proposition. Similar to Theorem *3.26 (Simp) of [WhiteheadRussell] p. 112. (Contributed by Jim Kingdon, 29-Mar-2018.)
Assertion
Ref Expression
simplimdc  |-  (DECID  ph  ->  ( -.  ( ph  ->  ps )  ->  ph ) )

Proof of Theorem simplimdc
StepHypRef Expression
1 pm2.21 607 . 2  |-  ( -. 
ph  ->  ( ph  ->  ps ) )
2 con1dc 842 . 2  |-  (DECID  ph  ->  ( ( -.  ph  ->  (
ph  ->  ps ) )  ->  ( -.  ( ph  ->  ps )  ->  ph ) ) )
31, 2mpi 15 1  |-  (DECID  ph  ->  ( -.  ( ph  ->  ps )  ->  ph ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4  DECID wdc 820
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 604  ax-in2 605  ax-io 699
This theorem depends on definitions:  df-bi 116  df-stab 817  df-dc 821
This theorem is referenced by:  pm2.5gdc  852  dfandc  870  pm4.79dc  889
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