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Theorem imaiun 5992
 Description: The image of an indexed union is the indexed union of the images. (Contributed by Mario Carneiro, 18-Jun-2014.)
Assertion
Ref Expression
imaiun
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem imaiun
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 rexcom4 2975 . . . 4
2 vex 2959 . . . . . 6
32elima3 5210 . . . . 5
43rexbii 2730 . . . 4
5 eliun 4097 . . . . . . 7
65anbi1i 677 . . . . . 6
7 r19.41v 2861 . . . . . 6
86, 7bitr4i 244 . . . . 5
98exbii 1592 . . . 4
101, 4, 93bitr4ri 270 . . 3
112elima3 5210 . . 3
12 eliun 4097 . . 3
1310, 11, 123bitr4i 269 . 2
1413eqriv 2433 1
 Colors of variables: wff set class Syntax hints:   wa 359  wex 1550   wceq 1652   wcel 1725  wrex 2706  cop 3817  ciun 4093  cima 4881 This theorem is referenced by:  imauni  5993  uniqs  6964  hsmexlem4  8309  hsmexlem5  8310  xkococnlem  17691  ismbf3d  19546  mbfimaopnlem  19547  i1fima  19570  i1fd  19573  itg1addlem5  19592  limciun  19781  sibfof  24654  itg2addnclem2  26257  ftc1anclem6  26285 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-iun 4095  df-br 4213  df-opab 4267  df-xp 4884  df-cnv 4886  df-dm 4888  df-rn 4889  df-res 4890  df-ima 4891
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