Theorem vsnid 3654

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 2766	. 2 |- x e. _V
2	1	snid 3653	1 |- x e. { x }

Syntax hints:   e. wcel 2167   {csn 3622

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-v 2765  df-sn 3628

This theorem is referenced by:  rext  4248  snnex  4483  dtruex  4595  fnressn  5748  fressnfv  5749  findcard2d  6952  findcard2sd  6953  diffifi  6955  ac6sfi  6959  fisseneq  6995  finomni  7206  cc2lem  7333  modfsummodlem1  11621  txdis  14513  txdis1cn  14514