Theorem vsnid 3705

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 2806	. 2 ⊢ 𝑥 ∈ V
2	1	snid 3704	1 ⊢ 𝑥 ∈ {𝑥}

Syntax hints:   ∈ wcel 2202  {csn 3673

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-v 2805  df-sn 3679

This theorem is referenced by:  rext  4313  snnex  4551  dtruex  4663  fnressn  5848  fressnfv  5849  findcard2d  7123  findcard2sd  7124  diffifi  7126  ac6sfi  7130  elssdc  7137  eqsndc  7138  fisseneq  7170  finomni  7399  cc2lem  7545  modfsummodlem1  12097  txdis  15088  txdis1cn  15089  gfsumcl  16816