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Theorem vsnid 3434
Description: A setvar variable is a member of its singleton (common case). (Contributed by David A. Wheeler, 8-Dec-2018.)
Assertion
Ref Expression
vsnid  |-  x  e. 
{ x }

Proof of Theorem vsnid
StepHypRef Expression
1 vex 2605 . 2  |-  x  e. 
_V
21snid 3433 1  |-  x  e. 
{ x }
Colors of variables: wff set class
Syntax hints:    e. wcel 1434   {csn 3406
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-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-sn 3412
This theorem is referenced by:  rext  3978  snnex  4207  dtruex  4310  fnressn  5381  fressnfv  5382  findcard2d  6425  findcard2sd  6426  diffifi  6428  ac6sfi  6431
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