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Theorem bdcnul 13599
Description: The empty class is bounded. See also bdcnulALT 13600. (Contributed by BJ, 3-Oct-2019.)
Assertion
Ref Expression
bdcnul  |- BOUNDED  (/)

Proof of Theorem bdcnul
StepHypRef Expression
1 noel 3409 . . 3  |-  -.  x  e.  (/)
21bdnth 13568 . 2  |- BOUNDED  x  e.  (/)
32bdelir 13581 1  |- BOUNDED  (/)
Colors of variables: wff set class
Syntax hints:    e. wcel 2135   (/)c0 3405  BOUNDED wbdc 13574
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 604  ax-in2 605  ax-io 699  ax-5 1434  ax-7 1435  ax-gen 1436  ax-ie1 1480  ax-ie2 1481  ax-8 1491  ax-10 1492  ax-11 1493  ax-i12 1494  ax-bndl 1496  ax-4 1497  ax-17 1513  ax-i9 1517  ax-ial 1521  ax-i5r 1522  ax-ext 2146  ax-bd0 13547  ax-bdim 13548  ax-bdn 13551  ax-bdeq 13554
This theorem depends on definitions:  df-bi 116  df-tru 1345  df-fal 1348  df-nf 1448  df-sb 1750  df-clab 2151  df-cleq 2157  df-clel 2160  df-nfc 2295  df-v 2724  df-dif 3114  df-nul 3406  df-bdc 13575
This theorem is referenced by:  bdeq0  13601
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