Theorem bdcvv 16556

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 2806	. . 3 ⊢ 𝑥 ∈ V
2	1	bdth 16530	. 2 ⊢ BOUNDED 𝑥 ∈ V
3	2	bdelir 16546	1 ⊢ BOUNDED V

Syntax hints:   ∈ wcel 2202  Vcvv 2803  BOUNDED wbdc 16539

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-ext 2213  ax-bd0 16512  ax-bdim 16513  ax-bdeq 16519

This theorem depends on definitions:  df-bi 117  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-v 2805  df-bdc 16540

This theorem is referenced by:  bdcnulALT  16565