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Theorem elriin 4370
 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 3650 . 2
2 eliin 4303 . . 3
32pm5.32i 642 . 2
41, 3bitri 253 1
 Colors of variables: wff setvar class Syntax hints:   wb 188   wa 371   wcel 1869  wral 2776   cin 3436  ciin 4298 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679  ax-5 1749  ax-6 1795  ax-7 1840  ax-10 1888  ax-11 1893  ax-12 1906  ax-13 2054  ax-ext 2401 This theorem depends on definitions:  df-bi 189  df-an 373  df-tru 1441  df-ex 1661  df-nf 1665  df-sb 1788  df-clab 2409  df-cleq 2415  df-clel 2418  df-nfc 2573  df-ral 2781  df-v 3084  df-in 3444  df-iin 4300 This theorem is referenced by:  limciun  22841  limcun  22842
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