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Theorem bdcnul 12874
Description: The empty class is bounded. See also bdcnulALT 12875. (Contributed by BJ, 3-Oct-2019.)
Assertion
Ref Expression
bdcnul BOUNDED

Proof of Theorem bdcnul
StepHypRef Expression
1 noel 3335 . . 3 ¬ 𝑥 ∈ ∅
21bdnth 12843 . 2 BOUNDED 𝑥 ∈ ∅
32bdelir 12856 1 BOUNDED
Colors of variables: wff set class
Syntax hints:  wcel 1463  c0 3331  BOUNDED wbdc 12849
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 586  ax-in2 587  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-bd0 12822  ax-bdim 12823  ax-bdn 12826  ax-bdeq 12829
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-fal 1320  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-dif 3041  df-nul 3332  df-bdc 12850
This theorem is referenced by:  bdeq0  12876
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