Theorem vsnid 3480

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 2623	. 2 ⊢ 𝑥 ∈ V
2	1	snid 3479	1 ⊢ 𝑥 ∈ {𝑥}

Syntax hints:   ∈ wcel 1439  {csn 3450

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071

This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-v 2622  df-sn 3456

This theorem is referenced by:  rext  4051  snnex  4283  dtruex  4388  fnressn  5497  fressnfv  5498  findcard2d  6661  findcard2sd  6662  diffifi  6664  ac6sfi  6668  fisseneq  6696  finomni  6857  modfsummodlem1  10911