Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  elriin Unicode version

Theorem elriin 3727
 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 3126 . 2
2 eliin 3662 . . 3
32pm5.32i 427 . 2
41, 3bitri 173 1
 Colors of variables: wff set class Syntax hints:   wa 97   wb 98   wcel 1393  wral 2306   cin 2916  ciin 3658 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-v 2559  df-in 2924  df-iin 3660 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator