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Theorem elsncg 3566
 Description: There is only one element in a singleton. Exercise 2 of [TakeutiZaring] p. 15 (generalized). (Contributed by NM, 13-Sep-1995.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
elsncg

Proof of Theorem elsncg
StepHypRef Expression
1 eqeq1 2259 . 2
2 df-sn 3550 . 2
31, 2elab2g 2853 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178   wceq 1619   wcel 1621  csn 3544 This theorem is referenced by:  elsnc  3567  elsni  3568  snidg  3569  eltpg  3580  eldifsn  3653  elsucg  4352  ltxr  10336  elfzp12  10739  ramcl  12950  lineval5a  25254  lineval6a  25255 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-v 2729  df-sn 3550
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