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

Theorem bddc 9283
Description: Decidability of a bounded formula is bounded. (Contributed by BJ, 3-Oct-2019.)
Hypothesis
Ref Expression
bdstab.1 BOUNDED
Assertion
Ref Expression
bddc BOUNDED DECID

Proof of Theorem bddc
StepHypRef Expression
1 bdstab.1 . . 3 BOUNDED
21ax-bdn 9272 . . 3 BOUNDED
31, 2ax-bdor 9271 . 2 BOUNDED
4 df-dc 742 . 2 DECID
53, 4bd0r 9280 1 BOUNDED DECID
Colors of variables: wff set class
Syntax hints:   wn 3   wo 628  DECID wdc 741  BOUNDED wbd 9267
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-bd0 9268  ax-bdor 9271  ax-bdn 9272
This theorem depends on definitions:  df-bi 110  df-dc 742
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator