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  5839  fressnfv  5840  findcard2d  7079  findcard2sd  7080  diffifi  7082  ac6sfi  7086  elssdc  7093  eqsndc  7094  fisseneq  7126  finomni  7338  cc2lem  7484  modfsummodlem1  12016  txdis  15000  txdis1cn  15001