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Theorem unidm 3125
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 707 . 2  |-  ( ( x  e.  A  \/  x  e.  A )  <->  x  e.  A )
21uneqri 3124 1  |-  ( A  u.  A )  =  A
Colors of variables: wff set class
Syntax hints:    = wceq 1285    e. wcel 1434    u. cun 2980
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-un 2986
This theorem is referenced by:  unundi  3143  unundir  3144  uneqin  3231  difabs  3244  dfsn2  3430  diftpsn3  3546  unisn  3637  dfdm2  4902  fun2  5115  resasplitss  5120  xpiderm  6264  pm54.43  6570
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