Theorem bdcvv 15992

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 2779	. . 3 |- x e. _V
2	1	bdth 15966	. 2 |- BOUNDED x e. _V
3	2	bdelir 15982	1 |- BOUNDED _V

Syntax hints:   e. wcel 2178   _Vcvv 2776  BOUNDED wbdc 15975

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 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-ext 2189  ax-bd0 15948  ax-bdim 15949  ax-bdeq 15955

This theorem depends on definitions:  df-bi 117  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-v 2778  df-bdc 15976

This theorem is referenced by:  bdcnulALT  16001