Theorem bdcvv 11236

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 2618	. . 3 ⊢ 𝑥 ∈ V
2	1	bdth 11210	. 2 ⊢ BOUNDED 𝑥 ∈ V
3	2	bdelir 11226	1 ⊢ BOUNDED V

Syntax hints:   ∈ wcel 1436  Vcvv 2615  BOUNDED wbdc 11219

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-ext 2067  ax-bd0 11192  ax-bdim 11193  ax-bdeq 11199

This theorem depends on definitions:  df-bi 115  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-v 2617  df-bdc 11220

This theorem is referenced by:  bdcnulALT  11245