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Theorem bdcsn 12891
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 12841 . . 3  |- BOUNDED  y  =  x
21bdcab 12870 . 2  |- BOUNDED  { y  |  y  =  x }
3 df-sn 3501 . 2  |-  { x }  =  { y  |  y  =  x }
42, 3bdceqir 12865 1  |- BOUNDED  { x }
Colors of variables: wff set class
Syntax hints:   {cab 2101   {csn 3495  BOUNDED wbdc 12861
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 12834  ax-bdeq 12841  ax-bdsb 12843
This theorem depends on definitions:  df-bi 116  df-clab 2102  df-cleq 2108  df-clel 2111  df-sn 3501  df-bdc 12862
This theorem is referenced by:  bdcpr  12892  bdctp  12893  bdvsn  12895  bdcsuc  12901
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