Theorem bdcnulALT 12023

Description: Alternate proof of bdcnul 12022. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 12001, or use the corresponding characterizations of its elements followed by bdelir 12004. (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 12014	. . 3 |- BOUNDED _V
2	1, 1	bdcdif 12018	. 2 |- BOUNDED ( _V \ _V )
3		df-nul 3288	. 2 |- (/) = ( _V \ _V )
4	2, 3	bdceqir 12001	1 |- BOUNDED (/)

Syntax hints:   _Vcvv 2620   \ cdif 2997   (/)c0 3287  BOUNDED wbdc 11997

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1382  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-ext 2071  ax-bd0 11970  ax-bdim 11971  ax-bdan 11972  ax-bdn 11974  ax-bdeq 11977  ax-bdsb 11979

This theorem depends on definitions:  df-bi 116  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-v 2622  df-dif 3002  df-nul 3288  df-bdc 11998

This theorem is referenced by: (None)