Theorem bdcvv 16178

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 2802	. . 3 ⊢ 𝑥 ∈ V
2	1	bdth 16152	. 2 ⊢ BOUNDED 𝑥 ∈ V
3	2	bdelir 16168	1 ⊢ BOUNDED V

Syntax hints:   ∈ wcel 2200  Vcvv 2799  BOUNDED wbdc 16161

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 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-ext 2211  ax-bd0 16134  ax-bdim 16135  ax-bdeq 16141

This theorem depends on definitions:  df-bi 117  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-v 2801  df-bdc 16162

This theorem is referenced by:  bdcnulALT  16187