Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bdcpw Unicode version

Theorem bdcpw 9432
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  ~P

Proof of Theorem bdcpw
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bdcpw.1 . . . 4 BOUNDED
21bdss 9427 . . 3 BOUNDED  C_
32bdcab 9412 . 2 BOUNDED  {  | 
C_  }
4 df-pw 3356 . 2  ~P  {  | 
C_  }
53, 4bdceqir 9407 1 BOUNDED  ~P
Colors of variables: wff set class
Syntax hints:   {cab 2026    C_ wss 2914   ~Pcpw 3354  BOUNDED wbdc 9403
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 9376  ax-bdal 9381  ax-bdsb 9385
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 2308  df-in 2921  df-ss 2928  df-pw 3356  df-bdc 9404
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator