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Theorem bd0 11184
Description: A formula equivalent to a bounded one is bounded. See also bd0r 11185. (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 11173 . 2  |-  (BOUNDED  ph  -> BOUNDED  ps )
41, 3ax-mp 7 1  |- BOUNDED  ps
Colors of variables: wff set class
Syntax hints:    <-> wb 103  BOUNDED wbd 11172
This theorem was proved from axioms:  ax-mp 7  ax-bd0 11173
This theorem is referenced by:  bd0r  11185  bdth  11191  bdnth  11194  bdnthALT  11195  bdph  11210  bdsbc  11218  bdsnss  11233  bdcint  11237  bdeqsuc  11241  bdcriota  11243  bj-axun2  11275
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