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Theorem sneqr 3966
 Description: If the singletons of two sets are equal, the two sets are equal. Part of Exercise 4 of [TakeutiZaring] p. 15. (Contributed by NM, 27-Aug-1993.)
Hypothesis
Ref Expression
sneqr.1
Assertion
Ref Expression
sneqr

Proof of Theorem sneqr
StepHypRef Expression
1 sneqr.1 . . . 4
21snid 3841 . . 3
3 eleq2 2497 . . 3
42, 3mpbii 203 . 2
51elsnc 3837 . 2
64, 5sylib 189 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1652   wcel 1725  cvv 2956  csn 3814 This theorem is referenced by:  snsssn  3967  sneqrg  3968  opth1  4434  opthwiener  4458  canth2  7260  axcc2lem  8316  dis2ndc  17523  axlowdim1  25898  wopprc  27101 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 2417 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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-sn 3820
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