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Theorem vsnid 3623
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 ∈ {𝑥}

Proof of Theorem vsnid
StepHypRef Expression
1 vex 2740 . 2 𝑥 ∈ V
21snid 3622 1 𝑥 ∈ {𝑥}
Colors of variables: wff set class
Syntax hints:  wcel 2148  {csn 3591
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-sn 3597
This theorem is referenced by:  rext  4211  snnex  4444  dtruex  4554  fnressn  5697  fressnfv  5698  findcard2d  6884  findcard2sd  6885  diffifi  6887  ac6sfi  6891  fisseneq  6924  finomni  7131  cc2lem  7243  modfsummodlem1  11435  txdis  13410  txdis1cn  13411
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