Theorem bdcnul 16564

Description: The empty class is bounded. See also bdcnulALT 16565. (Contributed by BJ, 3-Oct-2019.)

Assertion

Ref	Expression
bdcnul	⊢ BOUNDED ∅

Proof of Theorem bdcnul

Step	Hyp	Ref	Expression
1		noel 3500	. . 3 ⊢ ¬ 𝑥 ∈ ∅
2	1	bdnth 16533	. 2 ⊢ BOUNDED 𝑥 ∈ ∅
3	2	bdelir 16546	1 ⊢ BOUNDED ∅

Syntax hints:   ∈ wcel 2202  ∅c0 3496  BOUNDED wbdc 16539

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 2213  ax-bd0 16512  ax-bdim 16513  ax-bdn 16516  ax-bdeq 16519

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-fal 1404  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-v 2805  df-dif 3203  df-nul 3497  df-bdc 16540

This theorem is referenced by:  bdeq0  16566