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Theorem bdcsn 10819
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 10769 . . 3 BOUNDED 𝑦 = 𝑥
21bdcab 10798 . 2 BOUNDED {𝑦𝑦 = 𝑥}
3 df-sn 3412 . 2 {𝑥} = {𝑦𝑦 = 𝑥}
42, 3bdceqir 10793 1 BOUNDED {𝑥}
Colors of variables: wff set class
Syntax hints:  {cab 2068  {csn 3406  BOUNDED wbdc 10789
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 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468  ax-ext 2064  ax-bd0 10762  ax-bdeq 10769  ax-bdsb 10771
This theorem depends on definitions:  df-bi 115  df-clab 2069  df-cleq 2075  df-clel 2078  df-sn 3412  df-bdc 10790
This theorem is referenced by:  bdcpr  10820  bdctp  10821  bdvsn  10823  bdcsuc  10829
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