ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm4.62dc Unicode version

Theorem pm4.62dc 893
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 892 1  |-  (DECID  ph  ->  ( ( ph  ->  -.  ps )  <->  ( -.  ph  \/  -.  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 104    \/ wo 703  DECID wdc 829
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 609  ax-in2 610  ax-io 704
This theorem depends on definitions:  df-bi 116  df-dc 830
This theorem is referenced by:  ianordc  894
  Copyright terms: Public domain W3C validator