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Theorem inidm 3344
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 396 . 2 ((𝑥𝐴𝑥𝐴) ↔ 𝑥𝐴)
21ineqri 3328 1 (𝐴𝐴) = 𝐴
Colors of variables: wff set class
Syntax hints:   = wceq 1353  wcel 2148  cin 3128
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-in 3135
This theorem is referenced by:  inindi  3352  inindir  3353  uneqin  3386  ssdifeq0  3505  intsng  3876  xpindi  4758  xpindir  4759  resindm  4945  ofres  6091  offval2  6092  ofrfval2  6093  suppssof1  6094  ofco  6095  offveqb  6096  caofref  6098  caofrss  6101  caoftrn  6102  undifdc  6917  strressid  12509  ressinbasd  12512  baspartn  13208  epttop  13250  dvaddxxbr  13825  dvmulxxbr  13826  dvaddxx  13827  dvmulxx  13828  dviaddf  13829  dvimulf  13830
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