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Theorem imaundir 5369
Description: The image of a union. (Contributed by Jeff Hoffman, 17-Feb-2008.)
Assertion
Ref Expression
imaundir

Proof of Theorem imaundir
StepHypRef Expression
1 df-ima 4970 . . 3
2 resundir 5242 . . . 4
32rneqi 5183 . . 3
4 rnun 5364 . . 3
51, 3, 43eqtri 2487 . 2
6 df-ima 4970 . . 3
7 df-ima 4970 . . 3
86, 7uneq12i 3622 . 2
95, 8eqtr4i 2486 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1370  u.cun 3440  rancrn 4958  |`cres 4959  "cima 4960
This theorem is referenced by:  fvun  5884  suppun  6843  fsuppun  7774  fpwwe2lem13  8946  gsumzaddlemOLD  16571  funsnfsupOLD  17850  ustuqtop1  20215  mbfres2  21523  imadifxp  26407  eulerpartlemt  27210  bj-projun  33332
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-rab 2809  df-v 3083  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3752  df-if 3906  df-sn 3994  df-pr 3996  df-op 4000  df-br 4410  df-opab 4468  df-cnv 4965  df-dm 4967  df-rn 4968  df-res 4969  df-ima 4970
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