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Theorem iuncom4 3976
 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 2620 . . . . . . 7
21rexbii 2639 . . . . . 6
3 rexcom4 2878 . . . . . 6
42, 3bitri 240 . . . . 5
5 r19.41v 2764 . . . . . 6
65exbii 1582 . . . . 5
74, 6bitri 240 . . . 4
8 eluni2 3895 . . . . 5
98rexbii 2639 . . . 4
10 df-rex 2620 . . . . 5
11 eliun 3973 . . . . . . 7
1211anbi1i 676 . . . . . 6
1312exbii 1582 . . . . 5
1410, 13bitri 240 . . . 4
157, 9, 143bitr4i 268 . . 3
16 eliun 3973 . . 3
17 eluni2 3895 . . 3
1815, 16, 173bitr4i 268 . 2
1918eqriv 2350 1
 Colors of variables: wff setvar class Syntax hints:   wa 358  wex 1541   wceq 1642   wcel 1710  wrex 2615  cuni 3891  ciun 3969 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-ral 2619  df-rex 2620  df-v 2861  df-uni 3892  df-iun 3971 This theorem is referenced by: (None)
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