Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  iinss2 Unicode version

Theorem iinss2 3865
 Description: An indexed intersection is included in any of its members. (Contributed by FL, 15-Oct-2012.)
Assertion
Ref Expression
iinss2

Proof of Theorem iinss2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2689 . . . . 5
2 eliin 3818 . . . . 5
31, 2ax-mp 5 . . . 4
4 rsp 2480 . . . 4
53, 4sylbi 120 . . 3
65com12 30 . 2
76ssrdv 3103 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wcel 1480  wral 2416  cvv 2686   wss 3071  ciin 3814 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-v 2688  df-in 3077  df-ss 3084  df-iin 3816 This theorem is referenced by:  dmiin  4785
 Copyright terms: Public domain W3C validator