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

Theorem bdcvv 11236
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 2618 . . 3 𝑥 ∈ V
21bdth 11210 . 2 BOUNDED 𝑥 ∈ V
32bdelir 11226 1 BOUNDED V
Colors of variables: wff set class
Syntax hints:  wcel 1436  Vcvv 2615  BOUNDED wbdc 11219
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 11192  ax-bdim 11193  ax-bdeq 11199
This theorem depends on definitions:  df-bi 115  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-v 2617  df-bdc 11220
This theorem is referenced by:  bdcnulALT  11245
  Copyright terms: Public domain W3C validator