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

Theorem cokrelk 4284
Description: A Kuratowski composition is a Kuratowski relationship. (Contributed by SF, 4-Feb-2015.)
Assertion
Ref Expression
cokrelk k k

Proof of Theorem cokrelk
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-cok 4190 . . . . 5 k Ins2k Ins3k kk
21eleq2i 2417 . . . 4 k Ins2k Ins3k kk
3 vex 2862 . . . . 5
43elimakv 4260 . . . 4 Ins2k Ins3k kk Ins2k Ins3k k
52, 4bitri 240 . . 3 k Ins2k Ins3k k
6 inss1 3475 . . . . . 6 Ins2k Ins3k k Ins2k
76sseli 3269 . . . . 5 Ins2k Ins3k k Ins2k
8 vex 2862 . . . . . . 7
9 opkelins2kg 4251 . . . . . . 7 Ins2k
108, 3, 9mp2an 653 . . . . . 6 Ins2k
11 vex 2862 . . . . . . . . . . 11
12 vex 2862 . . . . . . . . . . 11
1311, 12opkelxpk 4248 . . . . . . . . . . 11 k
1411, 12, 13mpbir2an 886 . . . . . . . . . 10 k
15 eleq1 2413 . . . . . . . . . 10 k k
1614, 15mpbiri 224 . . . . . . . . 9 k
17163ad2ant2 977 . . . . . . . 8 k
1817exlimiv 1634 . . . . . . 7 k
1918exlimivv 1635 . . . . . 6 k
2010, 19sylbi 187 . . . . 5 Ins2k k
217, 20syl 15 . . . 4 Ins2k Ins3k k k
2221exlimiv 1634 . . 3 Ins2k Ins3k k k
235, 22sylbi 187 . 2 k k
2423ssriv 3277 1 k k
Colors of variables: wff setvar class
Syntax hints:   wb 176   w3a 934  wex 1541   wceq 1642   wcel 1710  cvv 2859   cin 3208   wss 3257  csn 3737  copk 4057   k cxpk 4174  kccnvk 4175   Ins2k cins2k 4176   Ins3k cins3k 4177  kcimak 4179   k ccomk 4180
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-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-ins2k 4187  df-imak 4189  df-cok 4190
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator