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Theorem dmuni 4573
 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 1570 . . . . 5
2 ancom 257 . . . . . . 7
3 19.41v 1798 . . . . . . 7
4 vex 2577 . . . . . . . . 9
54eldm2 4561 . . . . . . . 8
65anbi2i 438 . . . . . . 7
72, 3, 63bitr4i 205 . . . . . 6
87exbii 1512 . . . . 5
91, 8bitri 177 . . . 4
10 eluni 3611 . . . . 5
1110exbii 1512 . . . 4
12 df-rex 2329 . . . 4
139, 11, 123bitr4i 205 . . 3
144eldm2 4561 . . 3
15 eliun 3689 . . 3
1613, 14, 153bitr4i 205 . 2
1716eqriv 2053 1
 Colors of variables: wff set class Syntax hints:   wa 101   wceq 1259  wex 1397   wcel 1409  wrex 2324  cop 3406  cuni 3608  ciun 3685   cdm 4373 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-3an 898  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-ral 2328  df-rex 2329  df-v 2576  df-un 2950  df-sn 3409  df-pr 3410  df-op 3412  df-uni 3609  df-iun 3687  df-br 3793  df-dm 4383 This theorem is referenced by:  tfrlem8  5965  tfrlemi14d  5978
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