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Theorem fniunfv 6159
 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 5919 . . 3
21unieqd 4259 . 2
3 fvex 5881 . . 3
43dfiun2 4364 . 2
52, 4syl6reqr 2517 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  =wceq 1395  {cab 2442  E.wrex 2808  U.cuni 4249  U_ciun 4330  rancrn 5005  Fnwfn 5588  `cfv 5593 This theorem is referenced by:  funiunfv  6160  dffi3  7911  jech9.3  8253  hsmexlem5  8831  wuncval2  9146  dprdspan  17074  tgcmp  19901  txcmplem1  20142  txcmplem2  20143  xkococnlem  20160  alexsubALT  20551  bcth3  21770  ovolfioo  21879  ovolficc  21880  voliunlem2  21961  voliunlem3  21962  volsup  21966  uniiccdif  21987  uniioovol  21988  uniiccvol  21989  uniioombllem2  21992  uniioombllem4  21995  volsup2  22014  itg1climres  22121  itg2monolem1  22157  itg2gt0  22167  dftrpred2  29302  volsupnfl  30059  hbt  31079 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-sbc 3328  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-uni 4250  df-iun 4332  df-br 4453  df-opab 4511  df-mpt 4512  df-id 4800  df-xp 5010  df-rel 5011  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-iota 5556  df-fun 5595  df-fn 5596  df-fv 5601
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