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Theorem imaiun1 36314
 Description: The image of an indexed union is the indexed union of the images. (Contributed by RP, 29-Jun-2020.)
Assertion
Ref Expression
imaiun1
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem imaiun1
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 rexcom4 3053 . . . 4
2 vex 3034 . . . . . 6
32elima3 5181 . . . . 5
43rexbii 2881 . . . 4
5 eliun 4274 . . . . . . 7
65anbi2i 708 . . . . . 6
7 r19.42v 2931 . . . . . 6
86, 7bitr4i 260 . . . . 5
98exbii 1726 . . . 4
101, 4, 93bitr4ri 286 . . 3
112elima3 5181 . . 3
12 eliun 4274 . . 3
1310, 11, 123bitr4i 285 . 2
1413eqriv 2468 1
 Colors of variables: wff setvar class Syntax hints:   wa 376   wceq 1452  wex 1671   wcel 1904  wrex 2757  cop 3965  ciun 4269  cima 4842 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-iun 4271  df-br 4396  df-opab 4455  df-xp 4845  df-cnv 4847  df-dm 4849  df-rn 4850  df-res 4851  df-ima 4852 This theorem is referenced by:  trclimalb2  36389
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