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Theorem bdcnul 10351
 Description: The empty class is bounded. See also bdcnulALT 10352. (Contributed by BJ, 3-Oct-2019.)
Assertion
Ref Expression
bdcnul BOUNDED

Proof of Theorem bdcnul
StepHypRef Expression
1 noel 3255 . . 3 ¬ 𝑥 ∈ ∅
21bdnth 10320 . 2 BOUNDED 𝑥 ∈ ∅
32bdelir 10333 1 BOUNDED
 Colors of variables: wff set class Syntax hints:   ∈ wcel 1409  ∅c0 3251  BOUNDED wbdc 10326 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038  ax-bd0 10299  ax-bdim 10300  ax-bdn 10303  ax-bdeq 10306 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-fal 1265  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-dif 2947  df-nul 3252  df-bdc 10327 This theorem is referenced by:  bdeq0  10353
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