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Theorem unidm 3426
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 501 . 2  |-  ( ( x  e.  A  \/  x  e.  A )  <->  x  e.  A )
21uneqri 3425 1  |-  ( A  u.  A )  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1649    e. wcel 1717    u. cun 3254
This theorem is referenced by:  unundi  3444  unundir  3445  uneqin  3528  difabs  3541  undifabs  3641  dfif5  3687  dfsn2  3764  diftpsn3  3873  unisn  3966  dfdm2  5334  unixpid  5337  fun2  5541  resasplit  5546  xpider  6904  pm54.43  7813  lefld  14591  plyun0  19976  constr3trllem3  21480  probun  24449  filnetlem3  26093  mapfzcons  26456  diophin  26515  pwssplit1  26850  pwssplit4  26853  fiuneneq  27175  compne  27304
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2361
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2367  df-cleq 2373  df-clel 2376  df-nfc 2505  df-v 2894  df-un 3261
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