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Theorem snid 3394
Description: A set is a member of its singleton. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by NM, 31-Dec-1993.)
Hypothesis
Ref Expression
snid.1  _V
Assertion
Ref Expression
snid  { }

Proof of Theorem snid
StepHypRef Expression
1 snid.1 . 2  _V
2 snidb 3393 . 2  _V  { }
31, 2mpbi 133 1  { }
Colors of variables: wff set class
Syntax hints:   wcel 1390   _Vcvv 2551   {csn 3367
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-sn 3373
This theorem is referenced by:  ssnid  3395  exsnrex  3404  rabsnt  3436  sneqr  3522  rext  3942  unipw  3944  intid  3951  snnex  4147  ordtriexmidlem2  4209  ordtriexmid  4210  ordtri2orexmid  4211  regexmidlem1  4218  ordpwsucexmid  4246  opthprc  4334  fsn  5278  fsn2  5280  fvsn  5301  fvsnun1  5303  acexmidlema  5446  acexmidlemb  5447  acexmidlemab  5449  brtpos0  5808  en1  6215  elreal2  6708  1exp  8918  bj-d0clsepcl  9360
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