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Theorem 2iunin 3751
 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 3748 . . . 4
21a1i 9 . . 3
32iuneq2i 3703 . 2
4 iunin1 3749 . 2
53, 4eqtri 2076 1
 Colors of variables: wff set class Syntax hints:   wceq 1259   wcel 1409   cin 2944  ciun 3685 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-rex 2329  df-v 2576  df-in 2952  df-ss 2959  df-iun 3687 This theorem is referenced by: (None)
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