Theorem bdcnul 15478

Description: The empty class is bounded. See also bdcnulALT 15479. (Contributed by BJ, 3-Oct-2019.)

Assertion

Ref	Expression
bdcnul	⊢ BOUNDED ∅

Proof of Theorem bdcnul

Step	Hyp	Ref	Expression
1		noel 3454	. . 3 ⊢ ¬ 𝑥 ∈ ∅
2	1	bdnth 15447	. 2 ⊢ BOUNDED 𝑥 ∈ ∅
3	2	bdelir 15460	1 ⊢ BOUNDED ∅

Syntax hints:   ∈ wcel 2167  ∅c0 3450  BOUNDED wbdc 15453

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 710  ax-5 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178  ax-bd0 15426  ax-bdim 15427  ax-bdn 15430  ax-bdeq 15433

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-fal 1370  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-v 2765  df-dif 3159  df-nul 3451  df-bdc 15454

This theorem is referenced by:  bdeq0  15480