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Theorem bd3or 10336
Description: A disjunction of three bounded formulas is bounded. (Contributed by BJ, 3-Oct-2019.)
Hypotheses
Ref Expression
bd3or.1  |- BOUNDED  ph
bd3or.2  |- BOUNDED  ps
bd3or.3  |- BOUNDED  ch
Assertion
Ref Expression
bd3or  |- BOUNDED  ( ph  \/  ps  \/  ch )

Proof of Theorem bd3or
StepHypRef Expression
1 bd3or.1 . . . 4  |- BOUNDED  ph
2 bd3or.2 . . . 4  |- BOUNDED  ps
31, 2ax-bdor 10323 . . 3  |- BOUNDED  ( ph  \/  ps )
4 bd3or.3 . . 3  |- BOUNDED  ch
53, 4ax-bdor 10323 . 2  |- BOUNDED  ( ( ph  \/  ps )  \/  ch )
6 df-3or 897 . 2  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ( ph  \/  ps )  \/  ch ) )
75, 6bd0r 10332 1  |- BOUNDED  ( ph  \/  ps  \/  ch )
Colors of variables: wff set class
Syntax hints:    \/ wo 639    \/ w3o 895  BOUNDED wbd 10319
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-bd0 10320  ax-bdor 10323
This theorem depends on definitions:  df-bi 114  df-3or 897
This theorem is referenced by: (None)
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