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Theorem bdcnul 12990
Description: The empty class is bounded. See also bdcnulALT 12991. (Contributed by BJ, 3-Oct-2019.)
Assertion
Ref Expression
bdcnul  |- BOUNDED  (/)

Proof of Theorem bdcnul
StepHypRef Expression
1 noel 3337 . . 3  |-  -.  x  e.  (/)
21bdnth 12959 . 2  |- BOUNDED  x  e.  (/)
32bdelir 12972 1  |- BOUNDED  (/)
Colors of variables: wff set class
Syntax hints:    e. wcel 1465   (/)c0 3333  BOUNDED wbdc 12965
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 588  ax-in2 589  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099  ax-bd0 12938  ax-bdim 12939  ax-bdn 12942  ax-bdeq 12945
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-fal 1322  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-dif 3043  df-nul 3334  df-bdc 12966
This theorem is referenced by:  bdeq0  12992
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