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Theorem dmiun 5079
 Description: The domain of an indexed union. (Contributed by Mario Carneiro, 26-Apr-2016.)
Assertion
Ref Expression
dmiun

Proof of Theorem dmiun
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 rexcom4 2976 . . . 4
2 vex 2960 . . . . . 6
32eldm2 5069 . . . . 5
43rexbii 2731 . . . 4
5 eliun 4098 . . . . 5
65exbii 1593 . . . 4
71, 4, 63bitr4ri 271 . . 3
82eldm2 5069 . . 3
9 eliun 4098 . . 3
107, 8, 93bitr4i 270 . 2
1110eqriv 2434 1
 Colors of variables: wff set class Syntax hints:  wex 1551   wceq 1653   wcel 1726  wrex 2707  cop 3818  ciun 4094   cdm 4879 This theorem is referenced by:  dprd2d2  15603 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 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 2418 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ral 2711  df-rex 2712  df-rab 2715  df-v 2959  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824  df-iun 4096  df-br 4214  df-dm 4889
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