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Theorem bdcvv 12889
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 2661 . . 3 𝑥 ∈ V
21bdth 12863 . 2 BOUNDED 𝑥 ∈ V
32bdelir 12879 1 BOUNDED V
Colors of variables: wff set class
Syntax hints:  wcel 1463  Vcvv 2658  BOUNDED wbdc 12872
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 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-ext 2097  ax-bd0 12845  ax-bdim 12846  ax-bdeq 12852
This theorem depends on definitions:  df-bi 116  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-v 2660  df-bdc 12873
This theorem is referenced by:  bdcnulALT  12898
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