Theorem bdcnul 16635

Description: The empty class is bounded. See also bdcnulALT 16636. (Contributed by BJ, 3-Oct-2019.)

Assertion

Ref	Expression
bdcnul	⊢ BOUNDED ∅

Proof of Theorem bdcnul

Step	Hyp	Ref	Expression
1		noel 3512	. . 3 ⊢ ¬ 𝑥 ∈ ∅
2	1	bdnth 16604	. 2 ⊢ BOUNDED 𝑥 ∈ ∅
3	2	bdelir 16617	1 ⊢ BOUNDED ∅

Syntax hints:   ∈ wcel 2203  ∅c0 3508  BOUNDED wbdc 16610

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 619  ax-in2 620  ax-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2214  ax-bd0 16583  ax-bdim 16584  ax-bdn 16587  ax-bdeq 16590

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-fal 1404  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-nfc 2373  df-v 2815  df-dif 3213  df-nul 3509  df-bdc 16611

This theorem is referenced by:  bdeq0  16637