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Theorem bdcnul 13077
Description: The empty class is bounded. See also bdcnulALT 13078. (Contributed by BJ, 3-Oct-2019.)
Assertion
Ref Expression
bdcnul  |- BOUNDED  (/)

Proof of Theorem bdcnul
StepHypRef Expression
1 noel 3367 . . 3  |-  -.  x  e.  (/)
21bdnth 13046 . 2  |- BOUNDED  x  e.  (/)
32bdelir 13059 1  |- BOUNDED  (/)
Colors of variables: wff set class
Syntax hints:    e. wcel 1480   (/)c0 3363  BOUNDED wbdc 13052
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 2121  ax-bd0 13025  ax-bdim 13026  ax-bdn 13029  ax-bdeq 13032
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-fal 1337  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-dif 3073  df-nul 3364  df-bdc 13053
This theorem is referenced by:  bdeq0  13079
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