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  4301  snnex  4539  dtruex  4651  fnressn  5825  fressnfv  5826  findcard2d  7053  findcard2sd  7054  diffifi  7056  ac6sfi  7060  fisseneq  7096  finomni  7307  cc2lem  7452  modfsummodlem1  11967  txdis  14951  txdis1cn  14952