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Theorem unex 4106
 Description: The union of two sets is a set. (Contributed by SF, 12-Jan-2015.)
Hypotheses
Ref Expression
boolex.1 A V
boolex.2 B V
Assertion
Ref Expression
unex (AB) V

Proof of Theorem unex
StepHypRef Expression
1 boolex.1 . 2 A V
2 boolex.2 . 2 B V
3 unexg 4101 . 2 ((A V B V) → (AB) V)
41, 2, 3mp2an 653 1 (AB) V
 Colors of variables: wff setvar class Syntax hints:   ∈ wcel 1710  Vcvv 2859   ∪ cun 3207 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 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  df-un 3214 This theorem is referenced by:  vvex  4109  prex  4112  addcexlem  4382  eladdc  4398  nnc0suc  4412  addcass  4415  nncaddccl  4419  nnsucelrlem1  4424  nndisjeq  4429  preaddccan2lem1  4454  ltfinex  4464  ltfintrilem1  4465  tfinrelkex  4487  evenfinex  4503  oddfinex  4504  evenoddnnnul  4514  evenodddisjlem1  4515  nnadjoinlem1  4519  nnadjoin  4520  nnadjoinpw  4521  sfindbl  4530  vfinspss  4551  phiexg  4571  opexg  4587  proj1exg  4591  proj2exg  4592  proj2op  4601  phialllem2  4617  setconslem5  4735  1stex  4739  swapex  4742  fncup  5813  cupex  5816  clos1basesuc  5882  connexex  5913  unen  6048  enprmaplem4  6079  ncaddccl  6144  ce0addcnnul  6179  leconnnc  6218  addcdi  6250  nncdiv3lem2  6276  nchoicelem6  6294  nchoicelem16  6304  nchoicelem18  6306  frecxp  6314
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