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Theorem bd0 15054
Description: A formula equivalent to a bounded one is bounded. See also bd0r 15055. (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 15043 . 2  |-  (BOUNDED  ph  -> BOUNDED  ps )
41, 3ax-mp 5 1  |- BOUNDED  ps
Colors of variables: wff set class
Syntax hints:    <-> wb 105  BOUNDED wbd 15042
This theorem was proved from axioms:  ax-mp 5  ax-bd0 15043
This theorem is referenced by:  bd0r  15055  bdth  15061  bdnth  15064  bdnthALT  15065  bdph  15080  bdsbc  15088  bdsnss  15103  bdcint  15107  bdeqsuc  15111  bdcriota  15113  bj-axun2  15145
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