Theorem bdcnul 13052

Description: The empty class is bounded. See also bdcnulALT 13053. (Contributed by BJ, 3-Oct-2019.)

Assertion

Ref	Expression
bdcnul	|- BOUNDED (/)

Proof of Theorem bdcnul

Step	Hyp	Ref	Expression
1		noel 3362	. . 3 |- -. x e. (/)
2	1	bdnth 13021	. 2 |- BOUNDED x e. (/)
3	2	bdelir 13034	1 |- BOUNDED (/)

Syntax hints:   e. wcel 1480   (/)c0 3358  BOUNDED wbdc 13027

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119  ax-bd0 13000  ax-bdim 13001  ax-bdn 13004  ax-bdeq 13007

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-dif 3068  df-nul 3359  df-bdc 13028

This theorem is referenced by:  bdeq0  13054