Theorem bdcnul 13985

Description: The empty class is bounded. See also bdcnulALT 13986. (Contributed by BJ, 3-Oct-2019.)

Assertion

Ref	Expression
bdcnul	⊢ BOUNDED ∅

Proof of Theorem bdcnul

Step	Hyp	Ref	Expression
1		noel 3419	. . 3 ⊢ ¬ 𝑥 ∈ ∅
2	1	bdnth 13954	. 2 ⊢ BOUNDED 𝑥 ∈ ∅
3	2	bdelir 13967	1 ⊢ BOUNDED ∅

Syntax hints:   ∈ wcel 2142  ∅c0 3415  BOUNDED wbdc 13960

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 610  ax-in2 611  ax-io 705  ax-5 1441  ax-7 1442  ax-gen 1443  ax-ie1 1487  ax-ie2 1488  ax-8 1498  ax-10 1499  ax-11 1500  ax-i12 1501  ax-bndl 1503  ax-4 1504  ax-17 1520  ax-i9 1524  ax-ial 1528  ax-i5r 1529  ax-ext 2153  ax-bd0 13933  ax-bdim 13934  ax-bdn 13937  ax-bdeq 13940

This theorem depends on definitions:  df-bi 116  df-tru 1352  df-fal 1355  df-nf 1455  df-sb 1757  df-clab 2158  df-cleq 2164  df-clel 2167  df-nfc 2302  df-v 2733  df-dif 3124  df-nul 3416  df-bdc 13961

This theorem is referenced by:  bdeq0  13987