Theorem bdcvv 13699

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 2728	. . 3 ⊢ 𝑥 ∈ V
2	1	bdth 13673	. 2 ⊢ BOUNDED 𝑥 ∈ V
3	2	bdelir 13689	1 ⊢ BOUNDED V

Syntax hints:   ∈ wcel 2136  Vcvv 2725  BOUNDED wbdc 13682

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 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-ext 2147  ax-bd0 13655  ax-bdim 13656  ax-bdeq 13662

This theorem depends on definitions:  df-bi 116  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-v 2727  df-bdc 13683

This theorem is referenced by:  bdcnulALT  13708