Theorem vsnid 3608

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 2729	. 2 ⊢ 𝑥 ∈ V
2	1	snid 3607	1 ⊢ 𝑥 ∈ {𝑥}

Syntax hints:   ∈ wcel 2136  {csn 3576

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1435  ax-7 1436  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-10 1493  ax-11 1494  ax-i12 1495  ax-bndl 1497  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-i5r 1523  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-tru 1346  df-nf 1449  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-nfc 2297  df-v 2728  df-sn 3582

This theorem is referenced by:  rext  4193  snnex  4426  dtruex  4536  fnressn  5671  fressnfv  5672  findcard2d  6857  findcard2sd  6858  diffifi  6860  ac6sfi  6864  fisseneq  6897  finomni  7104  cc2lem  7207  modfsummodlem1  11397  txdis  12927  txdis1cn  12928