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Theorem bdcnulALT 12991
Description: Alternate proof of bdcnul 12990. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 12969, or use the corresponding characterizations of its elements followed by bdelir 12972. (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 12982 . . 3  |- BOUNDED  _V
21, 1bdcdif 12986 . 2  |- BOUNDED  ( _V  \  _V )
3 df-nul 3334 . 2  |-  (/)  =  ( _V  \  _V )
42, 3bdceqir 12969 1  |- BOUNDED  (/)
Colors of variables: wff set class
Syntax hints:   _Vcvv 2660    \ cdif 3038   (/)c0 3333  BOUNDED wbdc 12965
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 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-ext 2099  ax-bd0 12938  ax-bdim 12939  ax-bdan 12940  ax-bdn 12942  ax-bdeq 12945  ax-bdsb 12947
This theorem depends on definitions:  df-bi 116  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-v 2662  df-dif 3043  df-nul 3334  df-bdc 12966
This theorem is referenced by: (None)
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