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Theorem bd0r 11671
Description: A formula equivalent to a bounded one is bounded. Stated with a commuted (compared with bd0 11670) biconditional in the hypothesis, to work better with definitions (
ps is the definiendum that one wants to prove bounded). (Contributed by BJ, 3-Oct-2019.)
Hypotheses
Ref Expression
bd0r.min  |- BOUNDED  ph
bd0r.maj  |-  ( ps  <->  ph )
Assertion
Ref Expression
bd0r  |- BOUNDED  ps

Proof of Theorem bd0r
StepHypRef Expression
1 bd0r.min . 2  |- BOUNDED  ph
2 bd0r.maj . . 3  |-  ( ps  <->  ph )
32bicomi 130 . 2  |-  ( ph  <->  ps )
41, 3bd0 11670 1  |- BOUNDED  ps
Colors of variables: wff set class
Syntax hints:    <-> wb 103  BOUNDED wbd 11658
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 11659
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  bdbi  11672  bdstab  11673  bddc  11674  bd3or  11675  bd3an  11676  bdfal  11679  bdxor  11682  bj-bdcel  11683  bdab  11684  bdcdeq  11685  bdne  11699  bdnel  11700  bdreu  11701  bdrmo  11702  bdsbcALT  11705  bdss  11710  bdeq0  11713  bdvsn  11720  bdop  11721  bdeqsuc  11727  bj-bdind  11780
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