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Theorem bdcsn 10377
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 10327 . . 3  |- BOUNDED  y  =  x
21bdcab 10356 . 2  |- BOUNDED  { y  |  y  =  x }
3 df-sn 3409 . 2  |-  { x }  =  { y  |  y  =  x }
42, 3bdceqir 10351 1  |- BOUNDED  { x }
Colors of variables: wff set class
Syntax hints:   {cab 2042   {csn 3403  BOUNDED wbdc 10347
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-17 1435  ax-ial 1443  ax-ext 2038  ax-bd0 10320  ax-bdeq 10327  ax-bdsb 10329
This theorem depends on definitions:  df-bi 114  df-clab 2043  df-cleq 2049  df-clel 2052  df-sn 3409  df-bdc 10348
This theorem is referenced by:  bdcpr  10378  bdctp  10379  bdvsn  10381  bdcsuc  10387
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