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Theorem bdab 11072
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  ph
Assertion
Ref Expression
bdab  |- BOUNDED  x  e.  { y  |  ph }

Proof of Theorem bdab
StepHypRef Expression
1 bdab.1 . . 3  |- BOUNDED  ph
21ax-bdsb 11056 . 2  |- BOUNDED  [ x  /  y ] ph
3 df-clab 2070 . 2  |-  ( x  e.  { y  | 
ph }  <->  [ x  /  y ] ph )
42, 3bd0r 11059 1  |- BOUNDED  x  e.  { y  |  ph }
Colors of variables: wff set class
Syntax hints:    e. wcel 1434   [wsb 1687   {cab 2069  BOUNDED wbd 11046
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-bd0 11047  ax-bdsb 11056
This theorem depends on definitions:  df-bi 115  df-clab 2070
This theorem is referenced by:  bdcab  11083  bdsbcALT  11093
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