Theorem bdcnul 13900

Description: The empty class is bounded. See also bdcnulALT 13901. (Contributed by BJ, 3-Oct-2019.)

Assertion

Ref	Expression
bdcnul	|- BOUNDED (/)

Proof of Theorem bdcnul

Step	Hyp	Ref	Expression
1		noel 3418	. . 3 |- -. x e. (/)
2	1	bdnth 13869	. 2 |- BOUNDED x e. (/)
3	2	bdelir 13882	1 |- BOUNDED (/)

Syntax hints:   e. wcel 2141   (/)c0 3414  BOUNDED wbdc 13875

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 609  ax-in2 610  ax-io 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152  ax-bd0 13848  ax-bdim 13849  ax-bdn 13852  ax-bdeq 13855

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-fal 1354  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-dif 3123  df-nul 3415  df-bdc 13876

This theorem is referenced by:  bdeq0  13902