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Theorem inidm 3182
Description: Idempotent law for intersection of classes. Theorem 15 of [Suppes] p. 26. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
inidm (𝐴𝐴) = 𝐴

Proof of Theorem inidm
Dummy variable 𝑥 is distinct from all other variables.
StepHypRef Expression
1 anidm 388 . 2 ((𝑥𝐴𝑥𝐴) ↔ 𝑥𝐴)
21ineqri 3166 1 (𝐴𝐴) = 𝐴
Colors of variables: wff set class
Syntax hints:   = wceq 1285  wcel 1434  cin 2973
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-in 2980
This theorem is referenced by:  inindi  3190  inindir  3191  uneqin  3222  ssdifeq0  3332  intsng  3678  xpindi  4499  xpindir  4500  resindm  4680  ofres  5756  offval2  5757  ofrfval2  5758  suppssof1  5759  ofco  5760  offveqb  5761  caofref  5763  caofrss  5766  caoftrn  5767  undiffi  6443
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