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Theorem iuncom4 4100
 Description: Commutation of union with indexed union. (Contributed by Mario Carneiro, 18-Jan-2014.)
Assertion
Ref Expression
iuncom4

Proof of Theorem iuncom4
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-rex 2711 . . . . . . 7
21rexbii 2730 . . . . . 6
3 rexcom4 2975 . . . . . 6
42, 3bitri 241 . . . . 5
5 r19.41v 2861 . . . . . 6
65exbii 1592 . . . . 5
74, 6bitri 241 . . . 4
8 eluni2 4019 . . . . 5
98rexbii 2730 . . . 4
10 df-rex 2711 . . . . 5
11 eliun 4097 . . . . . . 7
1211anbi1i 677 . . . . . 6
1312exbii 1592 . . . . 5
1410, 13bitri 241 . . . 4
157, 9, 143bitr4i 269 . . 3
16 eliun 4097 . . 3
17 eluni2 4019 . . 3
1815, 16, 173bitr4i 269 . 2
1918eqriv 2433 1
 Colors of variables: wff set class Syntax hints:   wa 359  wex 1550   wceq 1652   wcel 1725  wrex 2706  cuni 4015  ciun 4093 This theorem is referenced by:  ituniiun  8302  tgidm  17045  txcmplem2  17674 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ral 2710  df-rex 2711  df-v 2958  df-uni 4016  df-iun 4095
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