Theorem bdcnul 14888

Description: The empty class is bounded. See also bdcnulALT 14889. (Contributed by BJ, 3-Oct-2019.)

Assertion

Ref	Expression
bdcnul	|- BOUNDED (/)

Proof of Theorem bdcnul

Step	Hyp	Ref	Expression
1		noel 3438	. . 3 |- -. x e. (/)
2	1	bdnth 14857	. 2 |- BOUNDED x e. (/)
3	2	bdelir 14870	1 |- BOUNDED (/)

Syntax hints:   e. wcel 2158   (/)c0 3434  BOUNDED wbdc 14863

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-in1 615  ax-in2 616  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169  ax-bd0 14836  ax-bdim 14837  ax-bdn 14840  ax-bdeq 14843

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-fal 1369  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-v 2751  df-dif 3143  df-nul 3435  df-bdc 14864

This theorem is referenced by:  bdeq0  14890