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Theorem 2iunin 3986
 Description: Rearrange indexed unions over intersection. (Contributed by NM, 18-Dec-2008.)
Assertion
Ref Expression
2iunin
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,)   ()   ()   ()

Proof of Theorem 2iunin
StepHypRef Expression
1 iunin2 3982 . . . 4
21a1i 10 . . 3
32iuneq2i 3939 . 2
4 iunin1 3983 . 2
53, 4eqtri 2316 1
 Colors of variables: wff set class Syntax hints:   wceq 1632   wcel 1696   cin 3164  ciun 3921 This theorem is referenced by:  fpar  6238 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ral 2561  df-rex 2562  df-v 2803  df-in 3172  df-ss 3179  df-iun 3923
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