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Theorem dmuni 5006
 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 1903 . . . . 5
2 ancom 451 . . . . . . 7
3 19.41v 1823 . . . . . . 7
4 vex 3025 . . . . . . . . 9
54eldm2 4995 . . . . . . . 8
65anbi2i 698 . . . . . . 7
72, 3, 63bitr4i 280 . . . . . 6
87exbii 1712 . . . . 5
91, 8bitri 252 . . . 4
10 eluni 4165 . . . . 5
1110exbii 1712 . . . 4
12 df-rex 2720 . . . 4
139, 11, 123bitr4i 280 . . 3
144eldm2 4995 . . 3
15 eliun 4247 . . 3
1613, 14, 153bitr4i 280 . 2
1716eqriv 2425 1
 Colors of variables: wff setvar class Syntax hints:   wa 370   wceq 1437  wex 1657   wcel 1872  wrex 2715  cop 3947  cuni 4162  ciun 4242   cdm 4796 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2063  ax-ext 2408 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2558  df-ral 2719  df-rex 2720  df-rab 2723  df-v 3024  df-dif 3382  df-un 3384  df-in 3386  df-ss 3393  df-nul 3705  df-if 3855  df-sn 3942  df-pr 3944  df-op 3948  df-uni 4163  df-iun 4244  df-br 4367  df-dm 4806 This theorem is referenced by:  wfrdmss  6997  wfrdmcl  6999  tfrlem8  7057  axdc3lem2  8832  bnj1400  29599  frrlem5d  30472  frrlem5e  30473  frrlem7  30475  nofulllem5  30544
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