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Theorem bdcsn 9433
Description: The singleton of a setvar is bounded. (Contributed by BJ, 16-Oct-2019.)
Assertion
Ref Expression
bdcsn BOUNDED  { }

Proof of Theorem bdcsn
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ax-bdeq 9383 . . 3 BOUNDED
21bdcab 9412 . 2 BOUNDED  {  |  }
3 df-sn 3376 . 2  { }  {  |  }
42, 3bdceqir 9407 1 BOUNDED  { }
Colors of variables: wff set class
Syntax hints:   {cab 2026   {csn 3370  BOUNDED wbdc 9403
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-4 1400  ax-17 1419  ax-ial 1427  ax-ext 2022  ax-bd0 9376  ax-bdeq 9383  ax-bdsb 9385
This theorem depends on definitions:  df-bi 110  df-clab 2027  df-cleq 2033  df-clel 2036  df-sn 3376  df-bdc 9404
This theorem is referenced by:  bdcpr  9434  bdctp  9435  bdvsn  9437  bdcsuc  9443
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