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Theorem unidm 3086
 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 674 . 2 ((𝑥𝐴𝑥𝐴) ↔ 𝑥𝐴)
21uneqri 3085 1 (𝐴𝐴) = 𝐴
 Colors of variables: wff set class Syntax hints:   = wceq 1243   ∈ wcel 1393   ∪ cun 2915 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922 This theorem is referenced by:  unundi  3104  unundir  3105  uneqin  3188  difabs  3201  dfsn2  3389  diftpsn3  3505  unisn  3596  dfdm2  4852  fun2  5064  resasplitss  5069  xpiderm  6177
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