Theorem bdcvv 14694

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 2742	. . 3 ⊢ 𝑥 ∈ V
2	1	bdth 14668	. 2 ⊢ BOUNDED 𝑥 ∈ V
3	2	bdelir 14684	1 ⊢ BOUNDED V

Syntax hints:   ∈ wcel 2148  Vcvv 2739  BOUNDED wbdc 14677

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 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-ext 2159  ax-bd0 14650  ax-bdim 14651  ax-bdeq 14657

This theorem depends on definitions:  df-bi 117  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-v 2741  df-bdc 14678

This theorem is referenced by:  bdcnulALT  14703