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Theorem dmiun 5037
 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 2935 . . . 4
2 vex 2919 . . . . . 6
32eldm2 5027 . . . . 5
43rexbii 2691 . . . 4
5 eliun 4057 . . . . 5
65exbii 1589 . . . 4
71, 4, 63bitr4ri 270 . . 3
82eldm2 5027 . . 3
9 eliun 4057 . . 3
107, 8, 93bitr4i 269 . 2
1110eqriv 2401 1
 Colors of variables: wff set class Syntax hints:  wex 1547   wceq 1649   wcel 1721  wrex 2667  cop 3777  ciun 4053   cdm 4837 This theorem is referenced by:  dprd2d2  15557 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ral 2671  df-rex 2672  df-rab 2675  df-v 2918  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-if 3700  df-sn 3780  df-pr 3781  df-op 3783  df-iun 4055  df-br 4173  df-dm 4847
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