Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  ssiun2 Unicode version

Theorem ssiun2 3856
 Description: Identity law for subset of an indexed union. (Contributed by NM, 12-Oct-2003.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
ssiun2

Proof of Theorem ssiun2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 rspe 2481 . . . 4
21ex 114 . . 3
3 eliun 3817 . . 3
42, 3syl6ibr 161 . 2
54ssrdv 3103 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1480  wrex 2417   wss 3071  ciun 3813 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-rex 2422  df-v 2688  df-in 3077  df-ss 3084  df-iun 3815 This theorem is referenced by:  ssiun2s  3857  triun  4039  ixpf  6614
 Copyright terms: Public domain W3C validator