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Theorem unidm 3260
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
StepHypRef Expression
1 oridm 502 . 2  |-  ( ( x  e.  A  \/  x  e.  A )  <->  x  e.  A )
21uneqri 3259 1  |-  ( A  u.  A )  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1619    e. wcel 1621    u. cun 3092
This theorem is referenced by:  unundi  3278  unundir  3279  uneqin  3362  difabs  3374  undifabs  3473  dfif5  3518  dfsn2  3595  unisn  3784  dfdm2  5156  unixpid  5159  fun2  5309  resasplit  5314  xpider  6663  pm54.43  7566  lefld  14275  plyun0  19506  domfldref  24392  inposet  24610  dispos  24619  pgapspf  25384  filnetlem3  25661  mapfzcons  26125  diophin  26184  pwssplit1  26520  pwssplit4  26523  fiuneneq  26845  compne  26975
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2237
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-v 2742  df-un 3099
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