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Theorem sneqbg 4200
 Description: Two singletons of sets are equal iff their elements are equal. (Contributed by Scott Fenton, 16-Apr-2012.)
Assertion
Ref Expression
sneqbg

Proof of Theorem sneqbg
StepHypRef Expression
1 sneqrg 4199 . 2
2 sneq 4039 . 2
31, 2impbid1 203 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  e.wcel 1818  {csn 4029 This theorem is referenced by:  suppval1  6924  suppsnop  6932  fseqdom  8428  infpwfidom  8430  canthwe  9050  s111  12623  mat1dimelbas  18973  mat1dimbas  18974  altopthg  29617  altopthbg  29618  initoid  32611  termoid  32612  embedsetcestrclem  32663  bj-snglc  34527 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-sn 4030
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