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Theorem bdcpw 11417
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 11412 . . 3 BOUNDED 𝑥𝐴
32bdcab 11397 . 2 BOUNDED {𝑥𝑥𝐴}
4 df-pw 3427 . 2 𝒫 𝐴 = {𝑥𝑥𝐴}
53, 4bdceqir 11392 1 BOUNDED 𝒫 𝐴
Colors of variables: wff set class
Syntax hints:  {cab 2074  wss 2997  𝒫 cpw 3425  BOUNDED wbdc 11388
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-11 1442  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-bd0 11361  ax-bdal 11366  ax-bdsb 11370
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-ral 2364  df-in 3003  df-ss 3010  df-pw 3427  df-bdc 11389
This theorem is referenced by: (None)
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