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Theorem 2iunin 4398
Description: Rearrange indexed unions over intersection. (Contributed by NM, 18-Dec-2008.)
Assertion
Ref Expression
2iunin
Distinct variable groups:   ,   ,   ,   ,

Proof of Theorem 2iunin
StepHypRef Expression
1 iunin2 4394 . . . 4
21a1i 11 . . 3
32iuneq2i 4349 . 2
4 iunin1 4395 . 2
53, 4eqtri 2486 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  e.wcel 1818  i^icin 3474  U_ciun 4330
This theorem is referenced by:  fpar  6904
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-in 3482  df-ss 3489  df-iun 4332
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