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Theorem opkex 4113
Description: A Kuratowski ordered pair exists. (Contributed by SF, 12-Jan-2015.)
Assertion
Ref Expression
opkex A, B V

Proof of Theorem opkex
StepHypRef Expression
1 df-opk 4058 . 2 A, B⟫ = {{A}, {A, B}}
2 prex 4112 . 2 {{A}, {A, B}} V
31, 2eqeltri 2423 1 A, B V
Colors of variables: wff setvar class
Syntax hints:   wcel 1710  Vcvv 2859  {csn 3737  {cpr 3738  copk 4057
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
This theorem is referenced by:  elxpk  4196  ssrelk  4211  eqrelk  4212  opkelopkabg  4245  otkelins2kg  4253  otkelins3kg  4254  opkelcokg  4261  opkelimagekg  4271  ins2kss  4279  ins3kss  4280  sikexlem  4295  dfimak2  4298  insklem  4304  ins2kexg  4305  ins3kexg  4306  dfint3  4318  ndisjrelk  4323  dfaddc2  4381  nnsucelrlem1  4424  nndisjeq  4429  ltfinex  4464  eqpwrelk  4478  eqpw1relk  4479  ncfinraiselem2  4480  ncfinlowerlem1  4482  eqtfinrelk  4486  evenfinex  4503  oddfinex  4504  evenodddisjlem1  4515  nnadjoinlem1  4519  nnpweqlem1  4522  srelk  4524  sfintfinlem1  4531  tfinnnlem1  4533  spfinex  4537  dfop2lem1  4573  setconslem2  4732  setconslem3  4733  setconslem4  4734  setconslem7  4737  df1st2  4738  dfswap2  4741
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