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Theorem pm4.62dc 798
Description: Implication in terms of disjunction. Like Theorem *4.62 of [WhiteheadRussell] p. 120, but for a decidable antecedent. (Contributed by Jim Kingdon, 21-Apr-2018.)
Assertion
Ref Expression
pm4.62dc  |-  (DECID  ph  ->  ( ( ph  ->  -.  ps )  <->  ( -.  ph  \/  -.  ps ) ) )

Proof of Theorem pm4.62dc
StepHypRef Expression
1 imordc 796 1  |-  (DECID  ph  ->  ( ( ph  ->  -.  ps )  <->  ( -.  ph  \/  -.  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 98    \/ wo 629  DECID wdc 742
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630
This theorem depends on definitions:  df-bi 110  df-dc 743
This theorem is referenced by:  ianordc  799
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