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Theorem bdcsn 14504
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 14454 . . 3  |- BOUNDED  y  =  x
21bdcab 14483 . 2  |- BOUNDED  { y  |  y  =  x }
3 df-sn 3598 . 2  |-  { x }  =  { y  |  y  =  x }
42, 3bdceqir 14478 1  |- BOUNDED  { x }
Colors of variables: wff set class
Syntax hints:   {cab 2163   {csn 3592  BOUNDED wbdc 14474
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534  ax-ext 2159  ax-bd0 14447  ax-bdeq 14454  ax-bdsb 14456
This theorem depends on definitions:  df-bi 117  df-clab 2164  df-cleq 2170  df-clel 2173  df-sn 3598  df-bdc 14475
This theorem is referenced by:  bdcpr  14505  bdctp  14506  bdvsn  14508  bdcsuc  14514
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