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Theorem fnima 5704
Description: The image of a function's domain is its range. (Contributed by NM, 4-Nov-2004.) (Proof shortened by Andrew Salmon, 17-Sep-2011.)
Assertion
Ref Expression
fnima

Proof of Theorem fnima
StepHypRef Expression
1 df-ima 5017 . 2
2 fnresdm 5695 . . 3
32rneqd 5235 . 2
41, 3syl5eq 2510 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  =wceq 1395  rancrn 5005  |`cres 5006  "cima 5007  Fnwfn 5588
This theorem is referenced by:  infdifsn  8094  carduniima  8498  cardinfima  8499  alephfp  8510  dprdf1o  17079  dprd2db  17092  lmhmrnlss  17696  mpfsubrg  18201  pf1subrg  18384  frlmlbs  18831  frlmup3  18834  ellspd  18836  ellspdOLD  18837  tgrest  19660  uniiccdif  21987  uniioombllem3  21994  dvgt0lem2  22404  eulerpartlemn  28320
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-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-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-br 4453  df-opab 4511  df-xp 5010  df-rel 5011  df-cnv 5012  df-dm 5014  df-rn 5015  df-res 5016  df-ima 5017  df-fun 5595  df-fn 5596
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