Theorem bdcvv 13044

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 2684	. . 3 ⊢ 𝑥 ∈ V
2	1	bdth 13018	. 2 ⊢ BOUNDED 𝑥 ∈ V
3	2	bdelir 13034	1 ⊢ BOUNDED V

Syntax hints:   ∈ wcel 1480  Vcvv 2681  BOUNDED wbdc 13027

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 2119  ax-bd0 13000  ax-bdim 13001  ax-bdeq 13007

This theorem depends on definitions:  df-bi 116  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-v 2683  df-bdc 13028

This theorem is referenced by:  bdcnulALT  13053