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Theorem bdcpw 9989
 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 9984 . . 3 BOUNDED 𝑥𝐴
32bdcab 9969 . 2 BOUNDED {𝑥𝑥𝐴}
4 df-pw 3361 . 2 𝒫 𝐴 = {𝑥𝑥𝐴}
53, 4bdceqir 9964 1 BOUNDED 𝒫 𝐴
 Colors of variables: wff set class Syntax hints:  {cab 2026   ⊆ wss 2917  𝒫 cpw 3359  BOUNDED wbdc 9960 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 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-bd0 9933  ax-bdal 9938  ax-bdsb 9942 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-ral 2311  df-in 2924  df-ss 2931  df-pw 3361  df-bdc 9961 This theorem is referenced by: (None)
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