Theorem bdcvv 11748

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

Step	Hyp	Ref	Expression
1		vex 2622	. . 3 |- x e. _V
2	1	bdth 11722	. 2 |- BOUNDED x e. _V
3	2	bdelir 11738	1 |- BOUNDED _V

Syntax hints:   e. wcel 1438   _Vcvv 2619  BOUNDED wbdc 11731

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 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-ext 2070  ax-bd0 11704  ax-bdim 11705  ax-bdeq 11711

This theorem depends on definitions:  df-bi 115  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-v 2621  df-bdc 11732

This theorem is referenced by:  bdcnulALT  11757