Theorem bdcvv 13892

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 2733	. . 3 ⊢ 𝑥 ∈ V
2	1	bdth 13866	. 2 ⊢ BOUNDED 𝑥 ∈ V
3	2	bdelir 13882	1 ⊢ BOUNDED V

Syntax hints:   ∈ wcel 2141  Vcvv 2730  BOUNDED wbdc 13875

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-ext 2152  ax-bd0 13848  ax-bdim 13849  ax-bdeq 13855

This theorem depends on definitions:  df-bi 116  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-v 2732  df-bdc 13876

This theorem is referenced by:  bdcnulALT  13901