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Theorem bdcnulALT 10373
Description: Alternate proof of bdcnul 10372. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 10351, or use the corresponding characterizations of its elements followed by bdelir 10354. (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 10364 . . 3  |- BOUNDED  _V
21, 1bdcdif 10368 . 2  |- BOUNDED  ( _V  \  _V )
3 df-nul 3253 . 2  |-  (/)  =  ( _V  \  _V )
42, 3bdceqir 10351 1  |- BOUNDED  (/)
Colors of variables: wff set class
Syntax hints:   _Vcvv 2574    \ cdif 2942   (/)c0 3252  BOUNDED wbdc 10347
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-ext 2038  ax-bd0 10320  ax-bdim 10321  ax-bdan 10322  ax-bdn 10324  ax-bdeq 10327  ax-bdsb 10329
This theorem depends on definitions:  df-bi 114  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-v 2576  df-dif 2948  df-nul 3253  df-bdc 10348
This theorem is referenced by: (None)
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