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Theorem elriin 4166
 Description: Elementhood in a relative intersection. (Contributed by Mario Carneiro, 30-Dec-2016.)
Assertion
Ref Expression
elriin
Distinct variable groups:   ,   ,   ,
Allowed substitution hint:   ()

Proof of Theorem elriin
StepHypRef Expression
1 elin 3532 . 2
2 eliin 4100 . . 3
32pm5.32i 620 . 2
41, 3bitri 242 1
 Colors of variables: wff set class Syntax hints:   wb 178   wa 360   wcel 1726  wral 2707   cin 3321  ciin 4096 This theorem is referenced by:  limciun  19786  limcun  19787 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-v 2960  df-in 3329  df-iin 4098
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