Theorem bdcnul 15935

Description: The empty class is bounded. See also bdcnulALT 15936. (Contributed by BJ, 3-Oct-2019.)

Assertion

Ref	Expression
bdcnul	⊢ BOUNDED ∅

Proof of Theorem bdcnul

Step	Hyp	Ref	Expression
1		noel 3468	. . 3 ⊢ ¬ 𝑥 ∈ ∅
2	1	bdnth 15904	. 2 ⊢ BOUNDED 𝑥 ∈ ∅
3	2	bdelir 15917	1 ⊢ BOUNDED ∅

Syntax hints:   ∈ wcel 2177  ∅c0 3464  BOUNDED wbdc 15910

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 615  ax-in2 616  ax-io 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2188  ax-bd0 15883  ax-bdim 15884  ax-bdn 15887  ax-bdeq 15890

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-fal 1379  df-nf 1485  df-sb 1787  df-clab 2193  df-cleq 2199  df-clel 2202  df-nfc 2338  df-v 2775  df-dif 3172  df-nul 3465  df-bdc 15911

This theorem is referenced by:  bdeq0  15937