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Theorem sikssvvk 4266
 Description: A Kuratowski singleton image is a Kuratowski relationship. (Contributed by SF, 13-Jan-2015.)
Assertion
Ref Expression
sikssvvk SIk A (V ×k V)

Proof of Theorem sikssvvk
Dummy variables x y z t u are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-sik 4192 . 2 SIk A = {x yz(x = ⟪y, z tu(y = {t} z = {u} t, u A))}
21opkabssvvki 4209 1 SIk A (V ×k V)
 Colors of variables: wff setvar class Syntax hints:   ∧ w3a 934  ∃wex 1541   = wceq 1642   ∈ wcel 1710  Vcvv 2859   ⊆ wss 3257  {csn 3737  ⟪copk 4057   ×k cxpk 4174   SIk csik 4181 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334  ax-nin 4078  ax-sn 4087 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ne 2518  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-un 3214  df-dif 3215  df-ss 3259  df-nul 3551  df-sn 3741  df-pr 3742  df-opk 4058  df-xpk 4185  df-sik 4192 This theorem is referenced by:  sikss1c1c  4267
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