Theorem bdcvv 15793

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 2775	. . 3 |- x e. _V
2	1	bdth 15767	. 2 |- BOUNDED x e. _V
3	2	bdelir 15783	1 |- BOUNDED _V

Syntax hints:   e. wcel 2176   _Vcvv 2772  BOUNDED wbdc 15776

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 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-ext 2187  ax-bd0 15749  ax-bdim 15750  ax-bdeq 15756

This theorem depends on definitions:  df-bi 117  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-v 2774  df-bdc 15777

This theorem is referenced by:  bdcnulALT  15802