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Theorem elsnc2g 4062
 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 4057 . 2
2 snidg 4058 . . 3
3 eleq1 2539 . . 3
42, 3syl5ibrcom 222 . 2
51, 4impbid2 204 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wceq 1379   wcel 1767  csn 4032 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3120  df-sn 4033 This theorem is referenced by:  elsnc2  4063  elsuc2g  4951  mptiniseg  5506  extmptsuppeq  6934  fzosplitsni  11898  limcco  22142  ply1termlem  22445  stirlinglem8  31672  dirkercncflem2  31695  elpmapat  34853
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