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Theorem bd0 13011
Description: A formula equivalent to a bounded one is bounded. See also bd0r 13012. (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 13000 . 2  |-  (BOUNDED  ph  -> BOUNDED  ps )
41, 3ax-mp 5 1  |- BOUNDED  ps
Colors of variables: wff set class
Syntax hints:    <-> wb 104  BOUNDED wbd 12999
This theorem was proved from axioms:  ax-mp 5  ax-bd0 13000
This theorem is referenced by:  bd0r  13012  bdth  13018  bdnth  13021  bdnthALT  13022  bdph  13037  bdsbc  13045  bdsnss  13060  bdcint  13064  bdeqsuc  13068  bdcriota  13070  bj-axun2  13102
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