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Theorem bdcsn 11418
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 11368 . . 3  |- BOUNDED  y  =  x
21bdcab 11397 . 2  |- BOUNDED  { y  |  y  =  x }
3 df-sn 3447 . 2  |-  { x }  =  { y  |  y  =  x }
42, 3bdceqir 11392 1  |- BOUNDED  { x }
Colors of variables: wff set class
Syntax hints:   {cab 2074   {csn 3441  BOUNDED wbdc 11388
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 11361  ax-bdeq 11368  ax-bdsb 11370
This theorem depends on definitions:  df-bi 115  df-clab 2075  df-cleq 2081  df-clel 2084  df-sn 3447  df-bdc 11389
This theorem is referenced by:  bdcpr  11419  bdctp  11420  bdvsn  11422  bdcsuc  11428
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