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Theorem dmun 4570
 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 3232 . . 3
2 brun 3838 . . . . . 6
32exbii 1512 . . . . 5
4 19.43 1535 . . . . 5
53, 4bitr2i 178 . . . 4
65abbii 2169 . . 3
71, 6eqtri 2076 . 2
8 df-dm 4383 . . 3
9 df-dm 4383 . . 3
108, 9uneq12i 3123 . 2
11 df-dm 4383 . 2
127, 10, 113eqtr4ri 2087 1
 Colors of variables: wff set class Syntax hints:   wo 639   wceq 1259  wex 1397  cab 2042   cun 2943   class class class wbr 3792   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-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2950  df-br 3793  df-dm 4383 This theorem is referenced by:  rnun  4760  dmpropg  4821  dmtpop  4824  fntpg  4983  fnun  5033
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