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Theorem unidm 3144
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 710 . 2  |-  ( ( x  e.  A  \/  x  e.  A )  <->  x  e.  A )
21uneqri 3143 1  |-  ( A  u.  A )  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1290    e. wcel 1439    u. cun 2998
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071
This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-v 2622  df-un 3004
This theorem is referenced by:  unundi  3162  unundir  3163  uneqin  3251  difabs  3264  dfsn2  3464  diftpsn3  3584  unisn  3675  dfdm2  4978  fun2  5197  resasplitss  5203  xpiderm  6377  pm54.43  6879
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