Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bddc Unicode version

Theorem bddc 11061
Description: Decidability of a bounded formula is bounded. (Contributed by BJ, 3-Oct-2019.)
Hypothesis
Ref Expression
bdstab.1  |- BOUNDED  ph
Assertion
Ref Expression
bddc  |- BOUNDED DECID  ph

Proof of Theorem bddc
StepHypRef Expression
1 bdstab.1 . . 3  |- BOUNDED  ph
21ax-bdn 11050 . . 3  |- BOUNDED  -.  ph
31, 2ax-bdor 11049 . 2  |- BOUNDED  ( ph  \/  -.  ph )
4 df-dc 777 . 2  |-  (DECID  ph  <->  ( ph  \/  -.  ph ) )
53, 4bd0r 11058 1  |- BOUNDED DECID  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3    \/ wo 662  DECID wdc 776  BOUNDED wbd 11045
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-bd0 11046  ax-bdor 11049  ax-bdn 11050
This theorem depends on definitions:  df-bi 115  df-dc 777
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator