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Theorem bd0 12949
Description: A formula equivalent to a bounded one is bounded. See also bd0r 12950. (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 12938 . 2  |-  (BOUNDED  ph  -> BOUNDED  ps )
41, 3ax-mp 5 1  |- BOUNDED  ps
Colors of variables: wff set class
Syntax hints:    <-> wb 104  BOUNDED wbd 12937
This theorem was proved from axioms:  ax-mp 5  ax-bd0 12938
This theorem is referenced by:  bd0r  12950  bdth  12956  bdnth  12959  bdnthALT  12960  bdph  12975  bdsbc  12983  bdsnss  12998  bdcint  13002  bdeqsuc  13006  bdcriota  13008  bj-axun2  13040
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