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Theorem bdcpw 12901
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 12896 . . 3 BOUNDED 𝑥𝐴
32bdcab 12881 . 2 BOUNDED {𝑥𝑥𝐴}
4 df-pw 3480 . 2 𝒫 𝐴 = {𝑥𝑥𝐴}
53, 4bdceqir 12876 1 BOUNDED 𝒫 𝐴
Colors of variables: wff set class
Syntax hints:  {cab 2101  wss 3039  𝒫 cpw 3478  BOUNDED wbdc 12872
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-11 1467  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-bd0 12845  ax-bdal 12850  ax-bdsb 12854
This theorem depends on definitions:  df-bi 116  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-ral 2396  df-in 3045  df-ss 3052  df-pw 3480  df-bdc 12873
This theorem is referenced by: (None)
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