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Theorem bdcvv 13044
Description: The universal class is bounded. The formulation may sound strange, but recall that here, "bounded" means "Δ0". (Contributed by BJ, 3-Oct-2019.)
Assertion
Ref Expression
bdcvv  |- BOUNDED  _V

Proof of Theorem bdcvv
StepHypRef Expression
1 vex 2684 . . 3  |-  x  e. 
_V
21bdth 13018 . 2  |- BOUNDED  x  e.  _V
32bdelir 13034 1  |- BOUNDED  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1480   _Vcvv 2681  BOUNDED wbdc 13027
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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-ext 2119  ax-bd0 13000  ax-bdim 13001  ax-bdeq 13007
This theorem depends on definitions:  df-bi 116  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-v 2683  df-bdc 13028
This theorem is referenced by:  bdcnulALT  13053
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