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Theorem elrint 4328
Description: Membership in a restricted intersection. (Contributed by Stefan O'Rear, 3-Apr-2015.)
Assertion
Ref Expression
elrint
Distinct variable groups:   ,   ,

Proof of Theorem elrint
StepHypRef Expression
1 elin 3686 . 2
2 elintg 4294 . . 3
32pm5.32i 637 . 2
41, 3bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  /\wa 369  e.wcel 1818  A.wral 2807  i^icin 3474  |^|cint 4286
This theorem is referenced by:  elrint2  4329  ptcnplem  20122  tmdgsum2  20595  limciun  22298
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ral 2812  df-v 3111  df-in 3482  df-int 4287
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