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Theorem iuncom 3758
 Description: Commutation of indexed unions. (Contributed by NM, 18-Dec-2008.)
Assertion
Ref Expression
iuncom
Distinct variable groups:   ,   ,   ,
Allowed substitution hints:   ()   ()   (,)

Proof of Theorem iuncom
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 rexcom 2545 . . . 4
2 eliun 3756 . . . . 5
32rexbii 2396 . . . 4
4 eliun 3756 . . . . 5
54rexbii 2396 . . . 4
61, 3, 53bitr4i 211 . . 3
7 eliun 3756 . . 3
8 eliun 3756 . . 3
96, 7, 83bitr4i 211 . 2
109eqriv 2092 1
 Colors of variables: wff set class Syntax hints:   wceq 1296   wcel 1445  wrex 2371  ciun 3752 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 668  ax-5 1388  ax-7 1389  ax-gen 1390  ax-ie1 1434  ax-ie2 1435  ax-8 1447  ax-10 1448  ax-11 1449  ax-i12 1450  ax-bndl 1451  ax-4 1452  ax-17 1471  ax-i9 1475  ax-ial 1479  ax-i5r 1480  ax-ext 2077 This theorem depends on definitions:  df-bi 116  df-tru 1299  df-nf 1402  df-sb 1700  df-clab 2082  df-cleq 2088  df-clel 2091  df-nfc 2224  df-ral 2375  df-rex 2376  df-v 2635  df-iun 3754 This theorem is referenced by: (None)
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