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Theorem elsnc2g 3834
 Description: There is only one element in a singleton. Exercise 2 of [TakeutiZaring] p. 15. This variation requires only that , rather than , be a set. (Contributed by NM, 28-Oct-2003.)
Assertion
Ref Expression
elsnc2g

Proof of Theorem elsnc2g
StepHypRef Expression
1 elsni 3830 . 2
2 snidg 3831 . . 3
3 eleq1 2495 . . 3
42, 3syl5ibrcom 214 . 2
51, 4impbid2 196 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wceq 1652   wcel 1725  csn 3806 This theorem is referenced by:  elsnc2  3835  elsuc2g  4641  mptiniseg  5355  fzosplitsni  11184  limcco  19768  ply1termlem  20110  stirlinglem8  27744  elpmapat  30400 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-sn 3812
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