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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
StepHypRef Expression
1 bdcvv 12014 . . 3  |- BOUNDED  _V
21, 1bdcdif 12018 . 2  |- BOUNDED  ( _V  \  _V )
3 df-nul 3288 . 2  |-  (/)  =  ( _V  \  _V )
42, 3bdceqir 12001 1  |- BOUNDED  (/)
Colors of variables: wff set class
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)
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