Theorem vsnid 3675

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 2779	. 2 |- x e. _V
2	1	snid 3674	1 |- x e. { x }

Syntax hints:   e. wcel 2178   {csn 3643

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-v 2778  df-sn 3649

This theorem is referenced by:  rext  4277  snnex  4513  dtruex  4625  fnressn  5793  fressnfv  5794  findcard2d  7014  findcard2sd  7015  diffifi  7017  ac6sfi  7021  fisseneq  7057  finomni  7268  cc2lem  7413  modfsummodlem1  11882  txdis  14864  txdis1cn  14865