ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  vsnid GIF version

Theorem vsnid 3592
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
StepHypRef Expression
1 vex 2715 . 2 𝑥 ∈ V
21snid 3591 1 𝑥 ∈ {𝑥}
Colors of variables: wff set class
Syntax hints:  wcel 2128  {csn 3560
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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139
This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-sn 3566
This theorem is referenced by:  rext  4176  snnex  4409  dtruex  4519  fnressn  5654  fressnfv  5655  findcard2d  6837  findcard2sd  6838  diffifi  6840  ac6sfi  6844  fisseneq  6877  finomni  7084  cc2lem  7187  modfsummodlem1  11357  txdis  12719  txdis1cn  12720
  Copyright terms: Public domain W3C validator