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Theorem idkex 4314
 Description: The Kuratowski identity relationship is a set. (Contributed by SF, 14-Jan-2015.)
Assertion
Ref Expression
idkex k

Proof of Theorem idkex
StepHypRef Expression
1 dfidk2 4313 . 2 k Sk k Sk
2 ssetkex 4294 . . 3 Sk
32cnvkex 4287 . . 3 k Sk
42, 3inex 4105 . 2 Sk k Sk
51, 4eqeltri 2423 1 k
 Colors of variables: wff setvar class Syntax hints:   wcel 1710  cvv 2859   cin 3208  kccnvk 4175   Sk cssetk 4183   k cidk 4184 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-xp 4079  ax-cnv 4080  ax-sset 4082  ax-sn 4087 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  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-ral 2619  df-rex 2620  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-cnvk 4186  df-ssetk 4193  df-idk 4195 This theorem is referenced by:  nnsucelrlem1  4424  nndisjeq  4429  tfinrelkex  4487  oddfinex  4504  evenodddisjlem1  4515  phiexg  4571  opexg  4587  proj1exg  4591  proj2exg  4592  setconslem5  4735  1stex  4739  swapex  4742
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