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Theorem bdcpw 14503
Description: The power class of a bounded class is bounded. (Contributed by BJ, 3-Oct-2019.)
Hypothesis
Ref Expression
bdcpw.1  |- BOUNDED  A
Assertion
Ref Expression
bdcpw  |- BOUNDED  ~P A

Proof of Theorem bdcpw
Dummy variable  x is distinct from all other variables.
StepHypRef Expression
1 bdcpw.1 . . . 4  |- BOUNDED  A
21bdss 14498 . . 3  |- BOUNDED  x  C_  A
32bdcab 14483 . 2  |- BOUNDED  { x  |  x 
C_  A }
4 df-pw 3577 . 2  |-  ~P A  =  { x  |  x 
C_  A }
53, 4bdceqir 14478 1  |- BOUNDED  ~P A
Colors of variables: wff set class
Syntax hints:   {cab 2163    C_ wss 3129   ~Pcpw 3575  BOUNDED wbdc 14474
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-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159  ax-bd0 14447  ax-bdal 14452  ax-bdsb 14456
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-ral 2460  df-in 3135  df-ss 3142  df-pw 3577  df-bdc 14475
This theorem is referenced by: (None)
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