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Theorem bdcsn 12902
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 12852 . . 3 BOUNDED 𝑦 = 𝑥
21bdcab 12881 . 2 BOUNDED {𝑦𝑦 = 𝑥}
3 df-sn 3501 . 2 {𝑥} = {𝑦𝑦 = 𝑥}
42, 3bdceqir 12876 1 BOUNDED {𝑥}
Colors of variables: wff set class
Syntax hints:  {cab 2101  {csn 3495  BOUNDED wbdc 12872
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 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470  ax-17 1489  ax-ial 1497  ax-ext 2097  ax-bd0 12845  ax-bdeq 12852  ax-bdsb 12854
This theorem depends on definitions:  df-bi 116  df-clab 2102  df-cleq 2108  df-clel 2111  df-sn 3501  df-bdc 12873
This theorem is referenced by:  bdcpr  12903  bdctp  12904  bdvsn  12906  bdcsuc  12912
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