Theorem bdcnul 14702

Description: The empty class is bounded. See also bdcnulALT 14703. (Contributed by BJ, 3-Oct-2019.)

Assertion

Ref	Expression
bdcnul	⊢ BOUNDED ∅

Proof of Theorem bdcnul

Step	Hyp	Ref	Expression
1		noel 3428	. . 3 ⊢ ¬ 𝑥 ∈ ∅
2	1	bdnth 14671	. 2 ⊢ BOUNDED 𝑥 ∈ ∅
3	2	bdelir 14684	1 ⊢ BOUNDED ∅

Syntax hints:   ∈ wcel 2148  ∅c0 3424  BOUNDED wbdc 14677

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 614  ax-in2 615  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159  ax-bd0 14650  ax-bdim 14651  ax-bdn 14654  ax-bdeq 14657

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-fal 1359  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2741  df-dif 3133  df-nul 3425  df-bdc 14678

This theorem is referenced by:  bdeq0  14704