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Theorem iun0 4386
 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 3788 . . . . . 6
21a1i 11 . . . . 5
32nrex 2912 . . . 4
4 eliun 4335 . . . 4
53, 4mtbir 299 . . 3
65, 12false 350 . 2
76eqriv 2453 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  =wceq 1395  e.wcel 1818  E.wrex 2808   c0 3784  U_ciun 4330 This theorem is referenced by:  iununi  4415  funiunfv  6160  om0r  7208  kmlem11  8561  ituniiun  8823  voliunlem1  21960  ofpreima2  27508  sigaclfu2  28121  measvunilem0  28184  measvuni  28185  cvmscld  28718  trpred0  29319 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-rex 2813  df-v 3111  df-dif 3478  df-nul 3785  df-iun 4332
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