Theorem vsnid 3621

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

Step	Hyp	Ref	Expression
1		vex 2738	. 2 |- x e. _V
2	1	snid 3620	1 |- x e. { x }

Syntax hints:   e. wcel 2146   {csn 3589

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 1445  ax-7 1446  ax-gen 1447  ax-ie1 1491  ax-ie2 1492  ax-8 1502  ax-10 1503  ax-11 1504  ax-i12 1505  ax-bndl 1507  ax-4 1508  ax-17 1524  ax-i9 1528  ax-ial 1532  ax-i5r 1533  ax-ext 2157

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1459  df-sb 1761  df-clab 2162  df-cleq 2168  df-clel 2171  df-nfc 2306  df-v 2737  df-sn 3595

This theorem is referenced by:  rext  4209  snnex  4442  dtruex  4552  fnressn  5694  fressnfv  5695  findcard2d  6881  findcard2sd  6882  diffifi  6884  ac6sfi  6888  fisseneq  6921  finomni  7128  cc2lem  7240  modfsummodlem1  11432  txdis  13348  txdis1cn  13349