Theorem vsnid 3698

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 2802	. 2 ⊢ 𝑥 ∈ V
2	1	snid 3697	1 ⊢ 𝑥 ∈ {𝑥}

Syntax hints:   ∈ wcel 2200  {csn 3666

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2801  df-sn 3672

This theorem is referenced by:  rext  4302  snnex  4540  dtruex  4652  fnressn  5832  fressnfv  5833  findcard2d  7066  findcard2sd  7067  diffifi  7069  ac6sfi  7073  elssdc  7080  eqsndc  7081  fisseneq  7112  finomni  7323  cc2lem  7468  modfsummodlem1  11988  txdis  14972  txdis1cn  14973