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

Step	Hyp	Ref	Expression
1		noel 3399	. . 3 ⊢ ¬ 𝑥 ∈ ∅
2	1	bdnth 13480	. 2 ⊢ BOUNDED 𝑥 ∈ ∅
3	2	bdelir 13493	1 ⊢ BOUNDED ∅

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