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Theorem bdcvv 11105
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 2617 . . 3  |-  x  e. 
_V
21bdth 11079 . 2  |- BOUNDED  x  e.  _V
32bdelir 11095 1  |- BOUNDED  _V
Colors of variables: wff set class
Syntax hints:    e. wcel 1436   _Vcvv 2614  BOUNDED wbdc 11088
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 1379  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-ext 2067  ax-bd0 11061  ax-bdim 11062  ax-bdeq 11068
This theorem depends on definitions:  df-bi 115  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-v 2616  df-bdc 11089
This theorem is referenced by:  bdcnulALT  11114
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