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Theorem bdcab 10798
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 10787 . 2  |- BOUNDED  y  e.  { x  |  ph }
32bdelir 10796 1  |- BOUNDED  { x  |  ph }
Colors of variables: wff set class
Syntax hints:   {cab 2068  BOUNDED wbd 10761  BOUNDED wbdc 10789
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 1379  ax-bd0 10762  ax-bdsb 10771
This theorem depends on definitions:  df-bi 115  df-clab 2069  df-bdc 10790
This theorem is referenced by:  bds  10800  bdcrab  10801  bdccsb  10809  bdcdif  10810  bdcun  10811  bdcin  10812  bdcpw  10818  bdcsn  10819  bdcuni  10825  bdcint  10826  bdciun  10827  bdciin  10828  bdcriota  10832  bj-bdfindis  10900
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