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Theorem complex 4104
 Description: The complement of a set is a set. (Contributed by SF, 12-Jan-2015.)
Hypothesis
Ref Expression
boolex.1 A V
Assertion
Ref Expression
complex A V

Proof of Theorem complex
StepHypRef Expression
1 boolex.1 . 2 A V
2 complexg 4099 . 2 (A V → ∼ A V)
31, 2ax-mp 8 1 A V
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 1710  Vcvv 2859   ∼ ccompl 3205 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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 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-v 2861  df-nin 3211  df-compl 3212 This theorem is referenced by:  vvex  4109  0ex  4110  imakexg  4299  intexg  4319  addcexlem  4382  nnsucelrlem1  4424  nndisjeq  4429  preaddccan2lem1  4454  ltfinex  4464  ssfin  4470  ncfinraiselem2  4480  ncfinlowerlem1  4482  tfinrelkex  4487  evenfinex  4503  oddfinex  4504  evenodddisjlem1  4515  nnadjoinlem1  4519  nnpweqlem1  4522  srelkex  4525  sfintfinlem1  4531  tfinnnlem1  4533  spfinex  4537  vfintle  4546  vfin1cltv  4547  nulnnn  4556  phiexg  4571  opexg  4587  proj1exg  4591  proj2exg  4592  setconslem5  4735  1stex  4739  swapex  4742  nfunv  5138  mptexlem  5810  disjex  5823  funsex  5828  fullfunexg  5859  transex  5910  refex  5911  antisymex  5912  connexex  5913  foundex  5914  extex  5915  symex  5916  endisj  6051  enprmaplem4  6079  nenpw1pwlem1  6084  ncaddccl  6144  tcdi  6164  ovcelem1  6171  ceex  6174  ce0nn  6180  tcfnex  6244  nclennlem1  6248  nmembers1lem1  6268  nnc3n3p1  6278  nchoicelem11  6299  nchoicelem16  6304  nchoicelem18  6306
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