Theorem bdcnul 16460

Description: The empty class is bounded. See also bdcnulALT 16461. (Contributed by BJ, 3-Oct-2019.)

Assertion

Ref	Expression
bdcnul	⊢ BOUNDED ∅

Proof of Theorem bdcnul

Step	Hyp	Ref	Expression
1		noel 3498	. . 3 ⊢ ¬ 𝑥 ∈ ∅
2	1	bdnth 16429	. 2 ⊢ BOUNDED 𝑥 ∈ ∅
3	2	bdelir 16442	1 ⊢ BOUNDED ∅

Syntax hints:   ∈ wcel 2202  ∅c0 3494  BOUNDED wbdc 16435

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213  ax-bd0 16408  ax-bdim 16409  ax-bdn 16412  ax-bdeq 16415

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-fal 1403  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-v 2804  df-dif 3202  df-nul 3495  df-bdc 16436

This theorem is referenced by:  bdeq0  16462