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Theorem bdcnulALT 14914
Description: Alternate proof of bdcnul 14913. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 14892, or use the corresponding characterizations of its elements followed by bdelir 14895. (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 14905 . . 3  |- BOUNDED  _V
21, 1bdcdif 14909 . 2  |- BOUNDED  ( _V  \  _V )
3 df-nul 3435 . 2  |-  (/)  =  ( _V  \  _V )
42, 3bdceqir 14892 1  |- BOUNDED  (/)
Colors of variables: wff set class
Syntax hints:   _Vcvv 2749    \ cdif 3138   (/)c0 3434  BOUNDED wbdc 14888
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 1457  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-ext 2169  ax-bd0 14861  ax-bdim 14862  ax-bdan 14863  ax-bdn 14865  ax-bdeq 14868  ax-bdsb 14870
This theorem depends on definitions:  df-bi 117  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-v 2751  df-dif 3143  df-nul 3435  df-bdc 14889
This theorem is referenced by: (None)
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