Theorem bdcnulALT 16461

Description: Alternate proof of bdcnul 16460. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 16439, or use the corresponding characterizations of its elements followed by bdelir 16442. (Contributed by BJ, 3-Oct-2019.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
bdcnulALT	⊢ BOUNDED ∅

Proof of Theorem bdcnulALT

Step	Hyp	Ref	Expression
1		bdcvv 16452	. . 3 ⊢ BOUNDED V
2	1, 1	bdcdif 16456	. 2 ⊢ BOUNDED (V ∖ V)
3		df-nul 3495	. 2 ⊢ ∅ = (V ∖ V)
4	2, 3	bdceqir 16439	1 ⊢ BOUNDED ∅

Syntax hints:  Vcvv 2802   ∖ cdif 3197  ∅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-5 1495  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-ext 2213  ax-bd0 16408  ax-bdim 16409  ax-bdan 16410  ax-bdn 16412  ax-bdeq 16415  ax-bdsb 16417

This theorem depends on definitions:  df-bi 117  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-v 2804  df-dif 3202  df-nul 3495  df-bdc 16436

This theorem is referenced by: (None)