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Theorem unidm 3080
 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 673 . 2 ((x A x A) ↔ x A)
21uneqri 3079 1 (AA) = A
 Colors of variables: wff set class Syntax hints:   = wceq 1242   ∈ wcel 1390   ∪ cun 2909 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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916 This theorem is referenced by:  unundi  3098  unundir  3099  uneqin  3182  difabs  3195  dfsn2  3381  diftpsn3  3496  unisn  3587  dfdm2  4795  fun2  5007  resasplitss  5012  xpiderm  6113
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