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Theorem bdcpw 10376
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 10371 . . 3  |- BOUNDED  x  C_  A
32bdcab 10356 . 2  |- BOUNDED  { x  |  x 
C_  A }
4 df-pw 3389 . 2  |-  ~P A  =  { x  |  x 
C_  A }
53, 4bdceqir 10351 1  |- BOUNDED  ~P A
Colors of variables: wff set class
Syntax hints:   {cab 2042    C_ wss 2945   ~Pcpw 3387  BOUNDED wbdc 10347
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-11 1413  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-bd0 10320  ax-bdal 10325  ax-bdsb 10329
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-ral 2328  df-in 2952  df-ss 2959  df-pw 3389  df-bdc 10348
This theorem is referenced by: (None)
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