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Theorem bdcnul 11756
Description: The empty class is bounded. See also bdcnulALT 11757. (Contributed by BJ, 3-Oct-2019.)
Assertion
Ref Expression
bdcnul  |- BOUNDED  (/)

Proof of Theorem bdcnul
StepHypRef Expression
1 noel 3290 . . 3  |-  -.  x  e.  (/)
21bdnth 11725 . 2  |- BOUNDED  x  e.  (/)
32bdelir 11738 1  |- BOUNDED  (/)
Colors of variables: wff set class
Syntax hints:    e. wcel 1438   (/)c0 3286  BOUNDED wbdc 11731
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-bd0 11704  ax-bdim 11705  ax-bdn 11708  ax-bdeq 11711
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-fal 1295  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-dif 3001  df-nul 3287  df-bdc 11732
This theorem is referenced by:  bdeq0  11758
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