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Theorem bdcpw 9324
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 9319 . . 3 BOUNDED xA
32bdcab 9304 . 2 BOUNDED {xxA}
4 df-pw 3353 . 2 𝒫 A = {xxA}
53, 4bdceqir 9299 1 BOUNDED 𝒫 A
Colors of variables: wff set class
Syntax hints:  {cab 2023  wss 2911  𝒫 cpw 3351  BOUNDED wbdc 9295
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-bd0 9268  ax-bdal 9273  ax-bdsb 9277
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-ral 2305  df-in 2918  df-ss 2925  df-pw 3353  df-bdc 9296
This theorem is referenced by: (None)
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