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Theorem bdcpw 10818
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 10813 . . 3 BOUNDED 𝑥𝐴
32bdcab 10798 . 2 BOUNDED {𝑥𝑥𝐴}
4 df-pw 3392 . 2 𝒫 𝐴 = {𝑥𝑥𝐴}
53, 4bdceqir 10793 1 BOUNDED 𝒫 𝐴
Colors of variables: wff set class
Syntax hints:  {cab 2068  wss 2974  𝒫 cpw 3390  BOUNDED wbdc 10789
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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-bd0 10762  ax-bdal 10767  ax-bdsb 10771
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-ral 2354  df-in 2980  df-ss 2987  df-pw 3392  df-bdc 10790
This theorem is referenced by: (None)
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