Theorem bdcvv 9977

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 2560	. . 3 ⊢ 𝑥 ∈ V
2	1	bdth 9951	. 2 ⊢ BOUNDED 𝑥 ∈ V
3	2	bdelir 9967	1 ⊢ BOUNDED V

Syntax hints:   ∈ wcel 1393  Vcvv 2557  BOUNDED wbdc 9960

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-ext 2022  ax-bd0 9933  ax-bdim 9934  ax-bdeq 9940

This theorem depends on definitions:  df-bi 110  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-v 2559  df-bdc 9961

This theorem is referenced by:  bdcnulALT  9986