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Theorem unidm 3116
 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 707 . 2 ((𝑥𝐴𝑥𝐴) ↔ 𝑥𝐴)
21uneqri 3115 1 (𝐴𝐴) = 𝐴
 Colors of variables: wff set class Syntax hints:   = wceq 1285   ∈ wcel 1434   ∪ cun 2972 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 2064 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604  df-un 2978 This theorem is referenced by:  unundi  3134  unundir  3135  uneqin  3222  difabs  3235  dfsn2  3420  diftpsn3  3535  unisn  3625  dfdm2  4882  fun2  5095  resasplitss  5100  xpiderm  6243  pm54.43  6518
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