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Theorem dmun 4741
 Description: The domain of a union is the union of domains. Exercise 56(a) of [Enderton] p. 65. (Contributed by NM, 12-Aug-1994.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Assertion
Ref Expression
dmun

Proof of Theorem dmun
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 unab 3338 . . 3
2 brun 3974 . . . . . 6
32exbii 1584 . . . . 5
4 19.43 1607 . . . . 5
53, 4bitr2i 184 . . . 4
65abbii 2253 . . 3
71, 6eqtri 2158 . 2
8 df-dm 4544 . . 3
9 df-dm 4544 . . 3
108, 9uneq12i 3223 . 2
11 df-dm 4544 . 2
127, 10, 113eqtr4ri 2169 1
 Colors of variables: wff set class Syntax hints:   wo 697   wceq 1331  wex 1468  cab 2123   cun 3064   class class class wbr 3924   cdm 4534 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-un 3070  df-br 3925  df-dm 4544 This theorem is referenced by:  rnun  4942  dmpropg  5006  dmtpop  5009  fntpg  5174  fnun  5224  sbthlemi5  6842  casedm  6964  djudm  6983  exmidfodomrlemim  7050  ennnfonelemhdmp1  11911  ennnfonelemkh  11914  strleund  12036  strleun  12037
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