New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  opkelidkg Unicode version

Theorem opkelidkg 4274
 Description: Membership in the Kuratowski identity relationship. (Contributed by SF, 13-Jan-2015.)
Assertion
Ref Expression
opkelidkg k

Proof of Theorem opkelidkg
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-idk 4195 . 2 k
2 eqeq1 2359 . 2
3 eqeq2 2362 . 2
41, 2, 3opkelopkabg 4245 1 k
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358   wceq 1642   wcel 1710  copk 4057   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-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-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-idk 4195 This theorem is referenced by:  dfidk2  4313  nnsucelrlem1  4424  nndisjeq  4429  eqtfinrelk  4486  oddfinex  4504  evenodddisjlem1  4515  dfphi2  4569
 Copyright terms: Public domain W3C validator