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Theorem bd0r 10883
Description: A formula equivalent to a bounded one is bounded. Stated with a commuted (compared with bd0 10882) biconditional in the hypothesis, to work better with definitions (𝜓 is the definiendum that one wants to prove bounded). (Contributed by BJ, 3-Oct-2019.)
Hypotheses
Ref Expression
bd0r.min BOUNDED 𝜑
bd0r.maj (𝜓𝜑)
Assertion
Ref Expression
bd0r BOUNDED 𝜓

Proof of Theorem bd0r
StepHypRef Expression
1 bd0r.min . 2 BOUNDED 𝜑
2 bd0r.maj . . 3 (𝜓𝜑)
32bicomi 130 . 2 (𝜑𝜓)
41, 3bd0 10882 1 BOUNDED 𝜓
Colors of variables: wff set class
Syntax hints:  wb 103  BOUNDED wbd 10870
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 10871
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  bdbi  10884  bdstab  10885  bddc  10886  bd3or  10887  bd3an  10888  bdfal  10891  bdxor  10894  bj-bdcel  10895  bdab  10896  bdcdeq  10897  bdne  10911  bdnel  10912  bdreu  10913  bdrmo  10914  bdsbcALT  10917  bdss  10922  bdeq0  10925  bdvsn  10932  bdop  10933  bdeqsuc  10939  bj-bdind  10992
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