Theorem bdcvv 13055

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 2689	. . 3 |- x e. _V
2	1	bdth 13029	. 2 |- BOUNDED x e. _V
3	2	bdelir 13045	1 |- BOUNDED _V

Syntax hints:   e. wcel 1480   _Vcvv 2686  BOUNDED wbdc 13038

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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-ext 2121  ax-bd0 13011  ax-bdim 13012  ax-bdeq 13018

This theorem depends on definitions:  df-bi 116  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-v 2688  df-bdc 13039

This theorem is referenced by:  bdcnulALT  13064