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Theorem elrint 3696
 Description: Membership in a restricted intersection. (Contributed by Stefan O'Rear, 3-Apr-2015.)
Assertion
Ref Expression
elrint
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem elrint
StepHypRef Expression
1 elin 3165 . 2
2 elintg 3664 . . 3
32pm5.32i 442 . 2
41, 3bitri 182 1
 Colors of variables: wff set class Syntax hints:   wa 102   wb 103   wcel 1434  wral 2353   cin 2981  cint 3656 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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-v 2612  df-in 2988  df-int 3657 This theorem is referenced by:  elrint2  3697
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