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Theorem unidm 3318
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 3317 1  |-  ( A  u.  A )  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1623    e. wcel 1684    u. cun 3150
This theorem is referenced by:  unundi  3336  unundir  3337  uneqin  3420  difabs  3432  undifabs  3531  dfif5  3577  dfsn2  3654  unisn  3843  dfdm2  5204  unixpid  5207  fun2  5406  resasplit  5411  xpider  6730  pm54.43  7633  lefld  14348  plyun0  19579  probun  23622  domfldref  25061  inposet  25278  dispos  25287  pgapspf  26052  filnetlem3  26329  mapfzcons  26793  diophin  26852  pwssplit1  27188  pwssplit4  27191  fiuneneq  27513  compne  27642  diftpsneq  28070
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-un 3157
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