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Theorem bdcab 15785
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 15774 . 2  |- BOUNDED  y  e.  { x  |  ph }
32bdelir 15783 1  |- BOUNDED  { x  |  ph }
Colors of variables: wff set class
Syntax hints:   {cab 2191  BOUNDED wbd 15748  BOUNDED wbdc 15776
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-gen 1472  ax-bd0 15749  ax-bdsb 15758
This theorem depends on definitions:  df-bi 117  df-clab 2192  df-bdc 15777
This theorem is referenced by:  bds  15787  bdcrab  15788  bdccsb  15796  bdcdif  15797  bdcun  15798  bdcin  15799  bdcpw  15805  bdcsn  15806  bdcuni  15812  bdcint  15813  bdciun  15814  bdciin  15815  bdcriota  15819  bj-bdfindis  15883
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