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Theorem unidm 3063
Description: Idempotent law for union of classes. Theorem 23 of [Suppes] p. 27. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
unidm (AA) = A

Proof of Theorem unidm
Dummy variable x is distinct from all other variables.
StepHypRef Expression
1 oridm 661 . 2 ((x A x A) ↔ x A)
21uneqri 3062 1 (AA) = A
Colors of variables: wff set class
Syntax hints:   = wceq 1228   wcel 1374  cun 2892
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-v 2537  df-un 2899
This theorem is referenced by:  unundi  3081  unundir  3082  uneqin  3165  difabs  3178  dfsn2  3364  diftpsn3  3479  unisn  3570  dfdm2  4779  fun2  4989  resasplitss  4994  xpiderm  6088
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