Theorem bdcvv 15931

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 2776	. . 3 ⊢ 𝑥 ∈ V
2	1	bdth 15905	. 2 ⊢ BOUNDED 𝑥 ∈ V
3	2	bdelir 15921	1 ⊢ BOUNDED V

Syntax hints:   ∈ wcel 2177  Vcvv 2773  BOUNDED wbdc 15914

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 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-ext 2188  ax-bd0 15887  ax-bdim 15888  ax-bdeq 15894

This theorem depends on definitions:  df-bi 117  df-sb 1787  df-clab 2193  df-cleq 2199  df-clel 2202  df-v 2775  df-bdc 15915

This theorem is referenced by:  bdcnulALT  15940