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Theorem bdcsn 15006
Description: The singleton of a setvar is bounded. (Contributed by BJ, 16-Oct-2019.)
Assertion
Ref Expression
bdcsn BOUNDED {𝑥}

Proof of Theorem bdcsn
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 ax-bdeq 14956 . . 3 BOUNDED 𝑦 = 𝑥
21bdcab 14985 . 2 BOUNDED {𝑦𝑦 = 𝑥}
3 df-sn 3613 . 2 {𝑥} = {𝑦𝑦 = 𝑥}
42, 3bdceqir 14980 1 BOUNDED {𝑥}
Colors of variables: wff set class
Syntax hints:  {cab 2175  {csn 3607  BOUNDED wbdc 14976
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 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-17 1537  ax-ial 1545  ax-ext 2171  ax-bd0 14949  ax-bdeq 14956  ax-bdsb 14958
This theorem depends on definitions:  df-bi 117  df-clab 2176  df-cleq 2182  df-clel 2185  df-sn 3613  df-bdc 14977
This theorem is referenced by:  bdcpr  15007  bdctp  15008  bdvsn  15010  bdcsuc  15016
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