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Theorem fnrnfv 5919
Description: The range of a function expressed as a collection of the function's values. (Contributed by NM, 20-Oct-2005.) (Proof shortened by Mario Carneiro, 31-Aug-2015.)
Assertion
Ref Expression
fnrnfv
Distinct variable groups:   , ,   , ,

Proof of Theorem fnrnfv
StepHypRef Expression
1 dffn5 5918 . . 3
2 rneq 5233 . . 3
31, 2sylbi 195 . 2
4 eqid 2457 . . 3
54rnmpt 5253 . 2
63, 5syl6eq 2514 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  =wceq 1395  {cab 2442  E.wrex 2808  e.cmpt 4510  rancrn 5005  Fnwfn 5588  `cfv 5593
This theorem is referenced by:  fvelrnb  5920  fniinfv  5932  dffo3  6046  fniunfv  6159  fnrnov  6448  pwcfsdom  8979  hauscmplem  19906  fargshiftfo  24638  grpoinvf  25242  fpwrelmapffslem  27555  meascnbl  28190  rnfdmpr  32308
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-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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