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Theorem fniinfv 5932
 Description: The indexed intersection of a function's values is the intersection of its range. (Contributed by NM, 20-Oct-2005.)
Assertion
Ref Expression
fniinfv
Distinct variable groups:   ,   ,

Proof of Theorem fniinfv
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 fnrnfv 5919 . . 3
21inteqd 4291 . 2
3 fvex 5881 . . 3
43dfiin2 4365 . 2
52, 4syl6reqr 2517 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  =wceq 1395  {cab 2442  E.wrex 2808  |^|cint 4286  |^|_ciin 4331  rancrn 5005  Fnwfn 5588  `cfv 5593 This theorem is referenced by:  firest  14830  pnrmopn  19844  txtube  20141  bcth3  21770  imaiinfv  30625  diaintclN  36785  dibintclN  36894  dihintcl  37071 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-int 4287  df-iin 4333  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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