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Theorem fniunfv 6089
Description: The indexed union of a function's values is the union of its range. Compare Definition 5.4 of [Monk1] p. 50. (Contributed by NM, 27-Sep-2004.)
Assertion
Ref Expression
fniunfv
Distinct variable groups:   ,   ,

Proof of Theorem fniunfv
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 fnrnfv 5861 . . 3
21unieqd 4218 . 2
3 fvex 5823 . . 3
43dfiun2 4321 . 2
52, 4syl6reqr 2514 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  =wceq 1370  {cab 2439  E.wrex 2801  U.cuni 4208  U_ciun 4288  rancrn 4958  Fnwfn 5532  `cfv 5537
This theorem is referenced by:  funiunfv  6090  dffi3  7817  jech9.3  8158  hsmexlem5  8736  wuncval2  9051  dprdspan  16699  tgcmp  19403  txcmplem1  19613  txcmplem2  19614  xkococnlem  19631  alexsubALT  20022  bcth3  21241  ovolfioo  21350  ovolficc  21351  voliunlem2  21432  voliunlem3  21433  volsup  21437  uniiccdif  21458  uniioovol  21459  uniiccvol  21460  uniioombllem2  21463  uniioombllem4  21466  volsup2  21485  itg1climres  21592  itg2monolem1  21628  itg2gt0  21638  dftrpred2  28139  volsupnfl  28896  hbt  29946
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-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-sep 4530  ax-nul 4538  ax-pr 4648
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-eu 2266  df-mo 2267  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-ral 2805  df-rex 2806  df-rab 2809  df-v 3083  df-sbc 3298  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-uni 4209  df-iun 4290  df-br 4410  df-opab 4468  df-mpt 4469  df-id 4753  df-xp 4963  df-rel 4964  df-cnv 4965  df-co 4966  df-dm 4967  df-rn 4968  df-iota 5500  df-fun 5539  df-fn 5540  df-fv 5545
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