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Theorem iuncom 4101
 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 2871 . . . 4
2 eliun 4099 . . . . 5
32rexbii 2732 . . . 4
4 eliun 4099 . . . . 5
54rexbii 2732 . . . 4
61, 3, 53bitr4i 270 . . 3
7 eliun 4099 . . 3
8 eliun 4099 . . 3
96, 7, 83bitr4i 270 . 2
109eqriv 2435 1
 Colors of variables: wff set class Syntax hints:   wceq 1653   wcel 1726  wrex 2708  ciun 4095 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ral 2712  df-rex 2713  df-v 2960  df-iun 4097
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