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Theorem sneqr 3680
 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 3571 . . 3
3 eleq2 2314 . . 3
42, 3mpbii 204 . 2
51elsnc 3567 . 2
64, 5sylib 190 1
 Colors of variables: wff set class Syntax hints:   wi 6   wceq 1619   wcel 1621  cvv 2727  csn 3544 This theorem is referenced by:  snsssn  3681  sneqrg  3682  opth1  4137  opthwiener  4161  canth2  6899  axcc2lem  7946  dis2ndc  17018  axlowdim1  23761  wopprc  26289 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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