Theorem vsnid 3651

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 2763	. 2 |- x e. _V
2	1	snid 3650	1 |- x e. { x }

Syntax hints:   e. wcel 2164   {csn 3619

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-v 2762  df-sn 3625

This theorem is referenced by:  rext  4245  snnex  4480  dtruex  4592  fnressn  5745  fressnfv  5746  findcard2d  6949  findcard2sd  6950  diffifi  6952  ac6sfi  6956  fisseneq  6990  finomni  7201  cc2lem  7328  modfsummodlem1  11602  txdis  14456  txdis1cn  14457