Theorem bdcvv 16452

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 2805	. . 3 ⊢ 𝑥 ∈ V
2	1	bdth 16426	. 2 ⊢ BOUNDED 𝑥 ∈ V
3	2	bdelir 16442	1 ⊢ BOUNDED V

Syntax hints:   ∈ wcel 2202  Vcvv 2802  BOUNDED wbdc 16435

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 1495  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-ext 2213  ax-bd0 16408  ax-bdim 16409  ax-bdeq 16415

This theorem depends on definitions:  df-bi 117  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-v 2804  df-bdc 16436

This theorem is referenced by:  bdcnulALT  16461