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Theorem unidm 3228
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 3227 1  |-  ( A  u.  A )  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1619    e. wcel 1621    u. cun 3076
This theorem is referenced by:  unundi  3246  unundir  3247  uneqin  3327  difabs  3339  undifabs  3437  dfif5  3482  dfsn2  3558  unisn  3743  dfdm2  5110  unixpid  5113  fun2  5263  resasplit  5268  xpider  6616  pm54.43  7517  lefld  14183  plyun0  19411  domfldref  24226  inposet  24444  dispos  24453  pgapspf  25218  filnetlem3  25495  mapfzcons  25959  diophin  26018  pwssplit1  26354  pwssplit4  26357  fiuneneq  26679  compne  26809
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 1926  ax-ext 2234
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 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-v 2729  df-un 3083
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