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Theorem inidm 3198
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 3182 1 (𝐴𝐴) = 𝐴
Colors of variables: wff set class
Syntax hints:   = wceq 1287  wcel 1436  cin 2987
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 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-v 2617  df-in 2994
This theorem is referenced by:  inindi  3206  inindir  3207  uneqin  3239  ssdifeq0  3352  intsng  3705  xpindi  4539  xpindir  4540  resindm  4721  ofres  5826  offval2  5827  ofrfval2  5828  suppssof1  5829  ofco  5830  offveqb  5831  caofref  5833  caofrss  5836  caoftrn  5837  undifdc  6586
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