Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  iun0 Unicode version

Theorem iun0 3878
 Description: An indexed union of the empty set is empty. (Contributed by NM, 26-Mar-2003.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
iun0

Proof of Theorem iun0
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 noel 3373 . . . . . 6
21a1i 9 . . . . 5
32nrex 2528 . . . 4
4 eliun 3826 . . . 4
53, 4mtbir 661 . . 3
65, 12false 691 . 2
76eqriv 2137 1
 Colors of variables: wff set class Syntax hints:   wn 3   wceq 1332   wcel 1481  wrex 2418  c0 3369  ciun 3822 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-in1 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-fal 1338  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-ral 2422  df-rex 2423  df-v 2692  df-dif 3079  df-nul 3370  df-iun 3824 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator