Theorem vsnid 3699

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 2803	. 2 ⊢ 𝑥 ∈ V
2	1	snid 3698	1 ⊢ 𝑥 ∈ {𝑥}

Syntax hints:   ∈ wcel 2200  {csn 3667

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 2802  df-sn 3673

This theorem is referenced by:  rext  4305  snnex  4543  dtruex  4655  fnressn  5835  fressnfv  5836  findcard2d  7073  findcard2sd  7074  diffifi  7076  ac6sfi  7080  elssdc  7087  eqsndc  7088  fisseneq  7119  finomni  7330  cc2lem  7475  modfsummodlem1  12007  txdis  14991  txdis1cn  14992