Theorem vsnid 3650

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 2763	. 2 ⊢ 𝑥 ∈ V
2	1	snid 3649	1 ⊢ 𝑥 ∈ {𝑥}

Syntax hints:   ∈ wcel 2164  {csn 3618

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-v 2762  df-sn 3624

This theorem is referenced by:  rext  4244  snnex  4479  dtruex  4591  fnressn  5744  fressnfv  5745  findcard2d  6947  findcard2sd  6948  diffifi  6950  ac6sfi  6954  fisseneq  6988  finomni  7199  cc2lem  7326  modfsummodlem1  11599  txdis  14445  txdis1cn  14446