Theorem bdcnul 15054

Description: The empty class is bounded. See also bdcnulALT 15055. (Contributed by BJ, 3-Oct-2019.)

Assertion

Ref	Expression
bdcnul	⊢ BOUNDED ∅

Proof of Theorem bdcnul

Step	Hyp	Ref	Expression
1		noel 3441	. . 3 ⊢ ¬ 𝑥 ∈ ∅
2	1	bdnth 15023	. 2 ⊢ BOUNDED 𝑥 ∈ ∅
3	2	bdelir 15036	1 ⊢ BOUNDED ∅

Syntax hints:   ∈ wcel 2160  ∅c0 3437  BOUNDED wbdc 15029

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171  ax-bd0 15002  ax-bdim 15003  ax-bdn 15006  ax-bdeq 15009

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-fal 1370  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-dif 3146  df-nul 3438  df-bdc 15030

This theorem is referenced by:  bdeq0  15056