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Theorem bdcvv 15294
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 2763 . . 3 𝑥 ∈ V
21bdth 15268 . 2 BOUNDED 𝑥 ∈ V
32bdelir 15284 1 BOUNDED V
Colors of variables: wff set class
Syntax hints:  wcel 2164  Vcvv 2760  BOUNDED wbdc 15277
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-ext 2175  ax-bd0 15250  ax-bdim 15251  ax-bdeq 15257
This theorem depends on definitions:  df-bi 117  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-v 2762  df-bdc 15278
This theorem is referenced by:  bdcnulALT  15303
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