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Theorem bd0r 9260
Description: A formula equivalent to a bounded one is bounded. Stated with a commuted (compared with bd0 9259) 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 123 . 2 (φψ)
41, 3bd0 9259 1 BOUNDED ψ
Colors of variables: wff set class
Syntax hints:  wb 98  BOUNDED wbd 9247
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 9248
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  bdbi  9261  bdstab  9262  bddc  9263  bd3or  9264  bd3an  9265  bdfal  9268  bdxor  9271  bj-bdcel  9272  bdab  9273  bdcdeq  9274  bdne  9288  bdnel  9289  bdreu  9290  bdrmo  9291  bdsbcALT  9294  bdss  9299  bdeq0  9302  bdvsn  9309  bdop  9310  bdeqsuc  9316  bj-bdind  9365
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