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Theorem dmuni 5079
 Description: The domain of a union. Part of Exercise 8 of [Enderton] p. 41. (Contributed by NM, 3-Feb-2004.)
Assertion
Ref Expression
dmuni
Distinct variable group:   ,

Proof of Theorem dmuni
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 excom 1756 . . . . 5
2 ancom 438 . . . . . . 7
3 19.41v 1924 . . . . . . 7
4 vex 2959 . . . . . . . . 9
54eldm2 5068 . . . . . . . 8
65anbi2i 676 . . . . . . 7
72, 3, 63bitr4i 269 . . . . . 6
87exbii 1592 . . . . 5
91, 8bitri 241 . . . 4
10 eluni 4018 . . . . 5
1110exbii 1592 . . . 4
12 df-rex 2711 . . . 4
139, 11, 123bitr4i 269 . . 3
144eldm2 5068 . . 3
15 eliun 4097 . . 3
1613, 14, 153bitr4i 269 . 2
1716eqriv 2433 1
 Colors of variables: wff set class Syntax hints:   wa 359  wex 1550   wceq 1652   wcel 1725  wrex 2706  cop 3817  cuni 4015  ciun 4093   cdm 4878 This theorem is referenced by:  tfrlem8  6645  axdc3lem2  8331  wfrlem7  25544  wfrlem9  25546  frrlem5d  25589  frrlem5e  25590  frrlem7  25592  nofulllem5  25661  bnj1400  29207 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-3an 938  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-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-uni 4016  df-iun 4095  df-br 4213  df-dm 4888
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