Theorem bdcnul 9985

Description: The empty class is bounded. See also bdcnulALT 9986. (Contributed by BJ, 3-Oct-2019.)

Assertion

Ref	Expression
bdcnul	⊢ BOUNDED ∅

Proof of Theorem bdcnul

Step	Hyp	Ref	Expression
1		noel 3228	. . 3 ⊢ ¬ 𝑥 ∈ ∅
2	1	bdnth 9954	. 2 ⊢ BOUNDED 𝑥 ∈ ∅
3	2	bdelir 9967	1 ⊢ BOUNDED ∅

Syntax hints:   ∈ wcel 1393  ∅c0 3224  BOUNDED wbdc 9960

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-bd0 9933  ax-bdim 9934  ax-bdn 9937  ax-bdeq 9940

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-dif 2920  df-nul 3225  df-bdc 9961

This theorem is referenced by:  bdeq0  9987