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Theorem bdcsn 9990
 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 9940 . . 3 BOUNDED 𝑦 = 𝑥
21bdcab 9969 . 2 BOUNDED {𝑦𝑦 = 𝑥}
3 df-sn 3381 . 2 {𝑥} = {𝑦𝑦 = 𝑥}
42, 3bdceqir 9964 1 BOUNDED {𝑥}
 Colors of variables: wff set class Syntax hints:  {cab 2026  {csn 3375  BOUNDED wbdc 9960 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 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427  ax-ext 2022  ax-bd0 9933  ax-bdeq 9940  ax-bdsb 9942 This theorem depends on definitions:  df-bi 110  df-clab 2027  df-cleq 2033  df-clel 2036  df-sn 3381  df-bdc 9961 This theorem is referenced by:  bdcpr  9991  bdctp  9992  bdvsn  9994  bdcsuc  10000
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