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Theorem bdcsn 9305
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 9255 . . 3 BOUNDED y = x
21bdcab 9284 . 2 BOUNDED {yy = x}
3 df-sn 3373 . 2 {x} = {yy = x}
42, 3bdceqir 9279 1 BOUNDED {x}
Colors of variables: wff set class
Syntax hints:  {cab 2023  {csn 3367  BOUNDED wbdc 9275
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-ext 2019  ax-bd0 9248  ax-bdeq 9255  ax-bdsb 9257
This theorem depends on definitions:  df-bi 110  df-clab 2024  df-cleq 2030  df-clel 2033  df-sn 3373  df-bdc 9276
This theorem is referenced by:  bdcpr  9306  bdctp  9307  bdvsn  9309  bdcsuc  9315
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