Theorem bdcvv 10648

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 2604	. . 3 ⊢ 𝑥 ∈ V
2	1	bdth 10622	. 2 ⊢ BOUNDED 𝑥 ∈ V
3	2	bdelir 10638	1 ⊢ BOUNDED V

Syntax hints:   ∈ wcel 1433  Vcvv 2601  BOUNDED wbdc 10631

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1376  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-ext 2063  ax-bd0 10604  ax-bdim 10605  ax-bdeq 10611

This theorem depends on definitions:  df-bi 115  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-v 2603  df-bdc 10632

This theorem is referenced by:  bdcnulALT  10657