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Theorem xpkex 4289
 Description: The Kuratowski cross product of two sets is a set. (Contributed by SF, 14-Jan-2015.)
Hypotheses
Ref Expression
xpkex.1
xpkex.2
Assertion
Ref Expression
xpkex k

Proof of Theorem xpkex
StepHypRef Expression
1 xpkex.1 . 2
2 xpkex.2 . 2
3 xpkexg 4288 . 2 k
41, 2, 3mp2an 653 1 k
 Colors of variables: wff setvar class Syntax hints:   wcel 1710  cvv 2859   k cxpk 4174 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-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 This theorem is referenced by:  sikexg  4296  imakexg  4299  ins2kexg  4305  ins3kexg  4306  imagekexg  4311  nnsucelrlem1  4424  ltfinex  4464  ssfin  4470  ncfinraiselem2  4480  ncfinlowerlem1  4482  tfinrelkex  4487  evenfinex  4503  oddfinex  4504  evenodddisjlem1  4515  nnadjoinlem1  4519  srelkex  4525  tfinnnlem1  4533  phiexg  4571  opexg  4587  proj1exg  4591  proj2exg  4592  setconslem5  4735  1stex  4739  swapex  4742  ssetex  4744  imaexg  4746  coexg  4749  siexg  4752
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