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Theorem bdcsn 12995
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 12945 . . 3 BOUNDED 𝑦 = 𝑥
21bdcab 12974 . 2 BOUNDED {𝑦𝑦 = 𝑥}
3 df-sn 3503 . 2 {𝑥} = {𝑦𝑦 = 𝑥}
42, 3bdceqir 12969 1 BOUNDED {𝑥}
Colors of variables: wff set class
Syntax hints:  {cab 2103  {csn 3497  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-4 1472  ax-17 1491  ax-ial 1499  ax-ext 2099  ax-bd0 12938  ax-bdeq 12945  ax-bdsb 12947
This theorem depends on definitions:  df-bi 116  df-clab 2104  df-cleq 2110  df-clel 2113  df-sn 3503  df-bdc 12966
This theorem is referenced by:  bdcpr  12996  bdctp  12997  bdvsn  12999  bdcsuc  13005
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