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Theorem sneqbg 4142
 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 4141 . 2
2 sneq 3982 . 2
31, 2impbid1 203 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wceq 1405   wcel 1842  csn 3972 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-v 3061  df-sn 3973 This theorem is referenced by:  suppval1  6908  suppsnop  6916  fseqdom  8439  infpwfidom  8441  canthwe  9059  s111  12677  initoid  15608  termoid  15609  embedsetcestrclem  15750  mat1dimelbas  19265  mat1dimbas  19266  altopthg  30305  altopthbg  30306  bj-snglc  31092  f1omptsnlem  31252
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