Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  eliin Unicode version

Theorem eliin 4336
 Description: Membership in indexed intersection. (Contributed by NM, 3-Sep-2003.)
Assertion
Ref Expression
eliin
Distinct variable group:   ,

Proof of Theorem eliin
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq1 2529 . . 3
21ralbidv 2896 . 2
3 df-iin 4333 . 2
42, 3elab2g 3248 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  e.wcel 1818  A.wral 2807  |^|_ciin 4331 This theorem is referenced by:  iinconst  4340  iuniin  4341  iinss1  4343  ssiinf  4379  iinss  4381  iinss2  4382  iinab  4391  iinun2  4396  iundif2  4397  iindif2  4399  iinin2  4400  elriin  4403  iinpw  4419  xpiindi  5143  cnviin  5549  iinpreima  6017  iiner  7402  ixpiin  7515  boxriin  7531  iunocv  18712  hauscmplem  19906  txtube  20141  isfcls  20510  iscmet3  21732  taylfval  22754  fnemeet1  30184  kelac1  31009  diaglbN  36782  dibglbN  36893  dihglbcpreN  37027 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-iin 4333
 Copyright terms: Public domain W3C validator