Theorem bdcvv 15657

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 2774	. . 3 ⊢ 𝑥 ∈ V
2	1	bdth 15631	. 2 ⊢ BOUNDED 𝑥 ∈ V
3	2	bdelir 15647	1 ⊢ BOUNDED V

Syntax hints:   ∈ wcel 2175  Vcvv 2771  BOUNDED wbdc 15640

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 1469  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-ext 2186  ax-bd0 15613  ax-bdim 15614  ax-bdeq 15620

This theorem depends on definitions:  df-bi 117  df-sb 1785  df-clab 2191  df-cleq 2197  df-clel 2200  df-v 2773  df-bdc 15641

This theorem is referenced by:  bdcnulALT  15666