Theorem vsnid 3655

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 2766	. 2 ⊢ 𝑥 ∈ V
2	1	snid 3654	1 ⊢ 𝑥 ∈ {𝑥}

Syntax hints:   ∈ wcel 2167  {csn 3623

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-10 1519  ax-11 1520  ax-i12 1521  ax-bndl 1523  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-nfc 2328  df-v 2765  df-sn 3629

This theorem is referenced by:  rext  4249  snnex  4484  dtruex  4596  fnressn  5751  fressnfv  5752  findcard2d  6961  findcard2sd  6962  diffifi  6964  ac6sfi  6968  fisseneq  7004  finomni  7215  cc2lem  7349  modfsummodlem1  11638  txdis  14597  txdis1cn  14598