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Theorem bdcab 12881
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 12870 . 2  |- BOUNDED  y  e.  { x  |  ph }
32bdelir 12879 1  |- BOUNDED  { x  |  ph }
Colors of variables: wff set class
Syntax hints:   {cab 2101  BOUNDED wbd 12844  BOUNDED wbdc 12872
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1408  ax-bd0 12845  ax-bdsb 12854
This theorem depends on definitions:  df-bi 116  df-clab 2102  df-bdc 12873
This theorem is referenced by:  bds  12883  bdcrab  12884  bdccsb  12892  bdcdif  12893  bdcun  12894  bdcin  12895  bdcpw  12901  bdcsn  12902  bdcuni  12908  bdcint  12909  bdciun  12910  bdciin  12911  bdcriota  12915  bj-bdfindis  12979
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