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Theorem bdcab 11397
Description: A class defined by class abstraction using a bounded formula is bounded. (Contributed by BJ, 6-Oct-2019.)
Hypothesis
Ref Expression
bdcab.1  |- BOUNDED  ph
Assertion
Ref Expression
bdcab  |- BOUNDED  { x  |  ph }

Proof of Theorem bdcab
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 bdcab.1 . . 3  |- BOUNDED  ph
21bdab 11386 . 2  |- BOUNDED  y  e.  { x  |  ph }
32bdelir 11395 1  |- BOUNDED  { x  |  ph }
Colors of variables: wff set class
Syntax hints:   {cab 2074  BOUNDED wbd 11360  BOUNDED wbdc 11388
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-gen 1383  ax-bd0 11361  ax-bdsb 11370
This theorem depends on definitions:  df-bi 115  df-clab 2075  df-bdc 11389
This theorem is referenced by:  bds  11399  bdcrab  11400  bdccsb  11408  bdcdif  11409  bdcun  11410  bdcin  11411  bdcpw  11417  bdcsn  11418  bdcuni  11424  bdcint  11425  bdciun  11426  bdciin  11427  bdcriota  11431  bj-bdfindis  11499
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