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Theorem pm2.5dc 837
Description: Negating an implication for a decidable antecedent. Theorem *2.5 of [WhiteheadRussell] p. 107 under a decidability condition. (Contributed by Jim Kingdon, 29-Mar-2018.)
Assertion
Ref Expression
pm2.5dc  |-  (DECID  ph  ->  ( -.  ( ph  ->  ps )  ->  ( -.  ph 
->  ps ) ) )

Proof of Theorem pm2.5dc
StepHypRef Expression
1 pm2.5gdc 836 1  |-  (DECID  ph  ->  ( -.  ( ph  ->  ps )  ->  ( -.  ph 
->  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4  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-in1 588  ax-in2 589  ax-io 683
This theorem depends on definitions:  df-bi 116  df-stab 801  df-dc 805
This theorem is referenced by:  pm5.11dc  879
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