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Theorem bdcnul 13511
Description: The empty class is bounded. See also bdcnulALT 13512. (Contributed by BJ, 3-Oct-2019.)
Assertion
Ref Expression
bdcnul BOUNDED

Proof of Theorem bdcnul
StepHypRef Expression
1 noel 3399 . . 3 ¬ 𝑥 ∈ ∅
21bdnth 13480 . 2 BOUNDED 𝑥 ∈ ∅
32bdelir 13493 1 BOUNDED
Colors of variables: wff set class
Syntax hints:  wcel 2128  c0 3395  BOUNDED wbdc 13486
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 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139  ax-bd0 13459  ax-bdim 13460  ax-bdn 13463  ax-bdeq 13466
This theorem depends on definitions:  df-bi 116  df-tru 1338  df-fal 1341  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-dif 3104  df-nul 3396  df-bdc 13487
This theorem is referenced by:  bdeq0  13513
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