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Theorem bdcsn 11407
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 11357 . . 3 BOUNDED 𝑦 = 𝑥
21bdcab 11386 . 2 BOUNDED {𝑦𝑦 = 𝑥}
3 df-sn 3447 . 2 {𝑥} = {𝑦𝑦 = 𝑥}
42, 3bdceqir 11381 1 BOUNDED {𝑥}
Colors of variables: wff set class
Syntax hints:  {cab 2074  {csn 3441  BOUNDED wbdc 11377
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-17 1464  ax-ial 1472  ax-ext 2070  ax-bd0 11350  ax-bdeq 11357  ax-bdsb 11359
This theorem depends on definitions:  df-bi 115  df-clab 2075  df-cleq 2081  df-clel 2084  df-sn 3447  df-bdc 11378
This theorem is referenced by:  bdcpr  11408  bdctp  11409  bdvsn  11411  bdcsuc  11417
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