Theorem bdcnul 13234

Description: The empty class is bounded. See also bdcnulALT 13235. (Contributed by BJ, 3-Oct-2019.)

Assertion

Ref	Expression
bdcnul	⊢ BOUNDED ∅

Proof of Theorem bdcnul

Step	Hyp	Ref	Expression
1		noel 3372	. . 3 ⊢ ¬ 𝑥 ∈ ∅
2	1	bdnth 13203	. 2 ⊢ BOUNDED 𝑥 ∈ ∅
3	2	bdelir 13216	1 ⊢ BOUNDED ∅

Syntax hints:   ∈ wcel 1481  ∅c0 3368  BOUNDED wbdc 13209

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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122  ax-bd0 13182  ax-bdim 13183  ax-bdn 13186  ax-bdeq 13189

This theorem depends on definitions:  df-bi 116  df-tru 1335  df-fal 1338  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2691  df-dif 3078  df-nul 3369  df-bdc 13210

This theorem is referenced by:  bdeq0  13236