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Theorem bd0 10773
Description: A formula equivalent to a bounded one is bounded. See also bd0r 10774. (Contributed by BJ, 3-Oct-2019.)
Hypotheses
Ref Expression
bd0.min  |- BOUNDED  ph
bd0.maj  |-  ( ph  <->  ps )
Assertion
Ref Expression
bd0  |- BOUNDED  ps

Proof of Theorem bd0
StepHypRef Expression
1 bd0.min . 2  |- BOUNDED  ph
2 bd0.maj . . 3  |-  ( ph  <->  ps )
32ax-bd0 10762 . 2  |-  (BOUNDED  ph  -> BOUNDED  ps )
41, 3ax-mp 7 1  |- BOUNDED  ps
Colors of variables: wff set class
Syntax hints:    <-> wb 103  BOUNDED wbd 10761
This theorem was proved from axioms:  ax-mp 7  ax-bd0 10762
This theorem is referenced by:  bd0r  10774  bdth  10780  bdnth  10783  bdnthALT  10784  bdph  10799  bdsbc  10807  bdsnss  10822  bdcint  10826  bdeqsuc  10830  bdcriota  10832  bj-axun2  10864
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