Theorem vsnid 3615

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 2733	. 2 ⊢ 𝑥 ∈ V
2	1	snid 3614	1 ⊢ 𝑥 ∈ {𝑥}

Syntax hints:   ∈ wcel 2141  {csn 3583

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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-sn 3589

This theorem is referenced by:  rext  4200  snnex  4433  dtruex  4543  fnressn  5682  fressnfv  5683  findcard2d  6869  findcard2sd  6870  diffifi  6872  ac6sfi  6876  fisseneq  6909  finomni  7116  cc2lem  7228  modfsummodlem1  11419  txdis  13071  txdis1cn  13072