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Theorem inidm 3140
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 376 . 2 ((x A x A) ↔ x A)
21ineqri 3124 1 (AA) = A
Colors of variables: wff set class
Syntax hints:   = wceq 1242   wcel 1390  cin 2910
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918
This theorem is referenced by:  inindi  3148  inindir  3149  uneqin  3182  ssdifeq0  3299  intsng  3640  xpindi  4414  xpindir  4415  ofres  5667  offval2  5668  ofrfval2  5669  suppssof1  5670  ofco  5671  offveqb  5672  caofref  5674  caofrss  5677  caoftrn  5678
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