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Theorem bdcnulALT 9986
 Description: Alternate proof of bdcnul 9985. Similarly, for the next few theorems proving boundedness of a class, one can either use their definition followed by bdceqir 9964, or use the corresponding characterizations of its elements followed by bdelir 9967. (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 9977 . . 3 BOUNDED V
21, 1bdcdif 9981 . 2 BOUNDED (V ∖ V)
3 df-nul 3225 . 2 ∅ = (V ∖ V)
42, 3bdceqir 9964 1 BOUNDED
 Colors of variables: wff set class Syntax hints:  Vcvv 2557   ∖ cdif 2914  ∅c0 3224  BOUNDED wbdc 9960 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-ext 2022  ax-bd0 9933  ax-bdim 9934  ax-bdan 9935  ax-bdn 9937  ax-bdeq 9940  ax-bdsb 9942 This theorem depends on definitions:  df-bi 110  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-v 2559  df-dif 2920  df-nul 3225  df-bdc 9961 This theorem is referenced by: (None)
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