Theorem bdcvv 16883

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 2824	. . 3 ⊢ 𝑥 ∈ V
2	1	bdth 16857	. 2 ⊢ BOUNDED 𝑥 ∈ V
3	2	bdelir 16873	1 ⊢ BOUNDED V

This proof depends on syntax axioms:   ∈ wcel 2209  Vcvv 2821  BOUNDED wbdc 16866

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-ext 2220  ax-bd0 16839  ax-bdim 16840  ax-bdeq 16846

This proof depends on definitions:  df-bi 117  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-v 2823  df-bdc 16867

This theorem is used by:  bdcnulALT  16892