Theorem vsnid 3701

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

Step	Hyp	Ref	Expression
1		vex 2805	. 2 ⊢ 𝑥 ∈ V
2	1	snid 3700	1 ⊢ 𝑥 ∈ {𝑥}

Syntax hints:   ∈ wcel 2202  {csn 3669

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-v 2804  df-sn 3675

This theorem is referenced by:  rext  4307  snnex  4545  dtruex  4657  fnressn  5840  fressnfv  5841  findcard2d  7080  findcard2sd  7081  diffifi  7083  ac6sfi  7087  elssdc  7094  eqsndc  7095  fisseneq  7127  finomni  7339  cc2lem  7485  modfsummodlem1  12035  txdis  15020  txdis1cn  15021  gfsumcl  16739