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Theorem bdcnulALT 13695
Description: Alternate proof of bdcnul 13694. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 13673, or use the corresponding characterizations of its elements followed by bdelir 13676. (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 13686 . . 3  |- BOUNDED  _V
21, 1bdcdif 13690 . 2  |- BOUNDED  ( _V  \  _V )
3 df-nul 3409 . 2  |-  (/)  =  ( _V  \  _V )
42, 3bdceqir 13673 1  |- BOUNDED  (/)
Colors of variables: wff set class
Syntax hints:   _Vcvv 2725    \ cdif 3112   (/)c0 3408  BOUNDED wbdc 13669
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-ext 2147  ax-bd0 13642  ax-bdim 13643  ax-bdan 13644  ax-bdn 13646  ax-bdeq 13649  ax-bdsb 13651
This theorem depends on definitions:  df-bi 116  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-v 2727  df-dif 3117  df-nul 3409  df-bdc 13670
This theorem is referenced by: (None)
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