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Theorem bdab 9273
Description: Membership in a class defined by class abstraction using a bounded formula, is a bounded formula. (Contributed by BJ, 3-Oct-2019.)
Hypothesis
Ref Expression
bdab.1 BOUNDED
Assertion
Ref Expression
bdab BOUNDED  {  |  }

Proof of Theorem bdab
StepHypRef Expression
1 bdab.1 . . 3 BOUNDED
21ax-bdsb 9257 . 2 BOUNDED
3 df-clab 2024 . 2  {  |  }
42, 3bd0r 9260 1 BOUNDED  {  |  }
Colors of variables: wff set class
Syntax hints:   wcel 1390  wsb 1642   {cab 2023  BOUNDED wbd 9247
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-bd0 9248  ax-bdsb 9257
This theorem depends on definitions:  df-bi 110  df-clab 2024
This theorem is referenced by:  bdcab  9284  bdsbcALT  9294
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