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Theorem snidg 3758
Description: A set is a member of its singleton. Part of Theorem 7.6 of [Quine] p. 49. (Contributed by NM, 28-Oct-2003.)
Assertion
Ref Expression
snidg (A VA {A})

Proof of Theorem snidg
StepHypRef Expression
1 eqid 2353 . 2 A = A
2 elsncg 3755 . 2 (A V → (A {A} ↔ A = A))
31, 2mpbiri 224 1 (A VA {A})
Colors of variables: wff setvar class
Syntax hints:  wi 4   = wceq 1642   wcel 1710  {csn 3737
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-sn 3741
This theorem is referenced by:  snidb  3759  elsnc2g  3761  snnzg  3833  opkth1g  4130  fvunsn  5444  nchoicelem6  6294  dmfrec  6316  frec0  6321
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