Theorem bdcvv 15470

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 2766	. . 3 ⊢ 𝑥 ∈ V
2	1	bdth 15444	. 2 ⊢ BOUNDED 𝑥 ∈ V
3	2	bdelir 15460	1 ⊢ BOUNDED V

Syntax hints:   ∈ wcel 2167  Vcvv 2763  BOUNDED wbdc 15453

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 1461  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-ext 2178  ax-bd0 15426  ax-bdim 15427  ax-bdeq 15433

This theorem depends on definitions:  df-bi 117  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-v 2765  df-bdc 15454

This theorem is referenced by:  bdcnulALT  15479