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Theorem bd0r 13053
Description: A formula equivalent to a bounded one is bounded. Stated with a commuted (compared with bd0 13052) 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 131 . 2 (𝜑𝜓)
41, 3bd0 13052 1 BOUNDED 𝜓
Colors of variables: wff set class
Syntax hints:  wb 104  BOUNDED wbd 13040
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-bd0 13041
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  bdbi  13054  bdstab  13055  bddc  13056  bd3or  13057  bd3an  13058  bdfal  13061  bdxor  13064  bj-bdcel  13065  bdab  13066  bdcdeq  13067  bdne  13081  bdnel  13082  bdreu  13083  bdrmo  13084  bdsbcALT  13087  bdss  13092  bdeq0  13095  bdvsn  13102  bdop  13103  bdeqsuc  13109  bj-bdind  13158
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