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Theorem bdcpw 12026
 Description: The power class of a bounded class is bounded. (Contributed by BJ, 3-Oct-2019.)
Hypothesis
Ref Expression
bdcpw.1 BOUNDED
Assertion
Ref Expression
bdcpw BOUNDED

Proof of Theorem bdcpw
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bdcpw.1 . . . 4 BOUNDED
21bdss 12021 . . 3 BOUNDED
32bdcab 12006 . 2 BOUNDED
4 df-pw 3435 . 2
53, 4bdceqir 12001 1 BOUNDED
 Colors of variables: wff set class Syntax hints:  cab 2075   wss 3000  cpw 3433  BOUNDED wbdc 11997 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-11 1443  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071  ax-bd0 11970  ax-bdal 11975  ax-bdsb 11979 This theorem depends on definitions:  df-bi 116  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-ral 2365  df-in 3006  df-ss 3013  df-pw 3435  df-bdc 11998 This theorem is referenced by: (None)
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