Theorem vsnid 3626

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 2742	. 2 ⊢ 𝑥 ∈ V
2	1	snid 3625	1 ⊢ 𝑥 ∈ {𝑥}

Syntax hints:   ∈ wcel 2148  {csn 3594

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 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2741  df-sn 3600

This theorem is referenced by:  rext  4217  snnex  4450  dtruex  4560  fnressn  5704  fressnfv  5705  findcard2d  6893  findcard2sd  6894  diffifi  6896  ac6sfi  6900  fisseneq  6933  finomni  7140  cc2lem  7267  modfsummodlem1  11466  txdis  13862  txdis1cn  13863