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Theorem inidm 3464
 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 625 . 2 ((x A x A) ↔ x A)
21ineqri 3449 1 (AA) = A
 Colors of variables: wff setvar class Syntax hints:   = wceq 1642   ∈ wcel 1710   ∩ cin 3208 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213 This theorem is referenced by:  inindi  3472  inindir  3473  uneqin  3506  ssdifeq0  3632  intsng  3961  xpindi  4864  xpindir  4865  xpassen  6057
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