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Theorem unidm 3331
Description: Idempotent law for union of classes. Theorem 23 of [Suppes] p. 27. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
unidm  |-  ( A  u.  A )  =  A

Proof of Theorem unidm
Dummy variable  x is distinct from all other variables.
StepHypRef Expression
1 oridm 500 . 2  |-  ( ( x  e.  A  \/  x  e.  A )  <->  x  e.  A )
21uneqri 3330 1  |-  ( A  u.  A )  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1632    e. wcel 1696    u. cun 3163
This theorem is referenced by:  unundi  3349  unundir  3350  uneqin  3433  difabs  3445  undifabs  3544  dfif5  3590  dfsn2  3667  diftpsn3  3772  unisn  3859  dfdm2  5220  unixpid  5223  fun2  5422  resasplit  5427  xpider  6746  pm54.43  7649  lefld  14364  plyun0  19595  probun  23637  domfldref  25164  inposet  25381  dispos  25390  pgapspf  26155  filnetlem3  26432  mapfzcons  26896  diophin  26955  pwssplit1  27291  pwssplit4  27294  fiuneneq  27616  compne  27745  constr3trllem3  28398
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-un 3170
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