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Definition df-rn 5671
Description: Define the range of a class. For example, 𝐹 = {⟨2, 6⟩, ⟨3, 9⟩} → ran 𝐹 = {6, 9} (ex-rn 30802). Contrast with domain (defined in df-dm 5670). For alternate definitions, see dfrn2 5877, dfrn3 5878, and dfrn4 6200. The notation "ran " is used by Enderton. The range of a function is often also called "the image of the function" (see definition in [Lang] p. ix), which can be justified by imadmrn 6071. Not to be confused with "codomain" (see df-f 6540), which may be a superset/superclass of the range (see frn 6713). (Contributed by NM, 1-Aug-1994.)
Assertion
Ref Expression
df-rn ran 𝐴 = dom 𝐴

Detailed syntax breakdown of Definition df-rn
StepHypRef Expression
1 cA . . 3 class 𝐴
21crn 5661 . 2 class ran 𝐴
31ccnv 5659 . . 3 class 𝐴
43cdm 5660 . 2 class dom 𝐴
52, 4wceq 1569 1 wff ran 𝐴 = dom 𝐴
Colors of variables:    wff setvar class
This definition is used by:  dfrn2  5877  dmcnvcnv  5922  rncnvcnv  5923  rneq  5925  rnss  5928  brelrng  5930  nfrn  5941  rncoss  5966  rncoeq  5970  cnvimarndm  6084  rnun  6141  rninOLD  6143  rnxp  6167  rnxpss  6169  imainrect  6178  rnsnopg  6221  cnvssrndm  6272  unidmrn  6280  dfdm2  6282  funcnvpr  6598  funcnvtp  6599  funcnvqp  6600  fncnv  6609  funcnvres  6614  funimacnv  6617  fimacnvdisj  6756  dff1o4  6829  foimacnv  6838  funcocnv2  6846  f1ompt  7106  nvof1o  7278  cnvexg  7919  tz7.48-3  8429  errn  8715  omxpenlem  9064  sbthlem5  9077  sbthlem8  9080  sbthlem9  9081  fodomr  9114  domss2  9122  fodomfir  9285  rnfi  9295  zorn2lem4  10489  rnct  10515  fpwwe2lem12  10633  trclublem  15039  relexpcnv  15079  relexpnnrn  15089  invf  17831  cicsym  17867  cnvtsr  18650  znleval  21715  ordtbas2  23359  ordtcnv  23369  ordtrest2  23372  cnconn  23590  tgqtop  23880  adj1o  32257  fcoinver  32960  fresf1o  32987  fcnvgreu  33028  dfcnv2  33031  preiman0  33066  gsumhashmul  33396  cycpmfvlem  33441  cycpmfv1  33442  cycpmfv2  33443  cycpmfv3  33444  cycpmrn  33472  cnvordtrestixx  34312  xrge0iifhmeo  34335  mbfmcst  34658  0rrv  34850  elrn3  36262  dfrn6  38985  cnvresrn  39025  dmxrn  39064  dmcoss2  39221  cnvrcl0  44379  conrel2d  44418  relexpaddss  44472  rntrclfvRP  44485  ntrneifv2  44834
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