Theorem bdcvv 15354

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 2763	. . 3 ⊢ 𝑥 ∈ V
2	1	bdth 15328	. 2 ⊢ BOUNDED 𝑥 ∈ V
3	2	bdelir 15344	1 ⊢ BOUNDED V

Syntax hints:   ∈ wcel 2164  Vcvv 2760  BOUNDED wbdc 15337

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 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-ext 2175  ax-bd0 15310  ax-bdim 15311  ax-bdeq 15317

This theorem depends on definitions:  df-bi 117  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-v 2762  df-bdc 15338

This theorem is referenced by:  bdcnulALT  15363