Theorem bdcnul 11639

Description: The empty class is bounded. See also bdcnulALT 11640. (Contributed by BJ, 3-Oct-2019.)

Assertion

Ref	Expression
bdcnul	⊢ BOUNDED ∅

Proof of Theorem bdcnul

Step	Hyp	Ref	Expression
1		noel 3290	. . 3 ⊢ ¬ 𝑥 ∈ ∅
2	1	bdnth 11608	. 2 ⊢ BOUNDED 𝑥 ∈ ∅
3	2	bdelir 11621	1 ⊢ BOUNDED ∅

Syntax hints:   ∈ wcel 1438  ∅c0 3286  BOUNDED wbdc 11614

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-bd0 11587  ax-bdim 11588  ax-bdn 11591  ax-bdeq 11594

This theorem depends on definitions:  df-bi 115  df-tru 1292  df-fal 1295  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-dif 3001  df-nul 3287  df-bdc 11615

This theorem is referenced by:  bdeq0  11641