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Definition df-rn 5658
Description: Define the range of a class. For example, 𝐹 = {⟨2, 6⟩, ⟨3, 9⟩} → ran 𝐹 = {6, 9} (ex-rn 30974). Contrast with domain (defined in df-dm 5657). For alternate definitions, see dfrn2 5866, dfrn3 5867, and dfrn4 6190. 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 6060. Not to be confused with "codomain" (see df-f 6531), which may be a superset/superclass of the range (see frn 6705). (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 5648 . 2 class ran 𝐴
31ccnv 5646 . . 3 class 𝐴
43cdm 5647 . 2 class dom 𝐴
52, 4wceq 1570 1 wff ran 𝐴 = dom 𝐴
Colors of variables:    wff setvar class
This definition is used by:  dfrn2  5866  dmcnvcnv  5911  rncnvcnv  5912  rneq  5914  rnss  5917  brelrng  5919  nfrn  5930  rncoss  5955  rncoeq  5959  cnvimarndm  6073  rnun  6130  rninOLD  6132  rnxp  6157  rnxpss  6159  imainrect  6168  rnsnopg  6211  cnvssrndm  6262  unidmrn  6271  dfdm2  6273  funcnvpr  6590  funcnvtp  6591  funcnvqp  6592  fncnv  6601  funcnvres  6606  funimacnv  6609  fimacnvdisj  6748  dff1o4  6821  foimacnv  6830  funcocnv2  6838  f1ompt  7099  nvof1o  7276  cnvexg  7919  tz7.48-3  8432  errn  8718  omxpenlem  9075  sbthlem5  9088  sbthlem8  9091  sbthlem9  9092  fodomr  9125  domss2  9133  fodomfir  9297  rnfi  9307  zorn2lem4  10548  rnct  10575  fpwwe2lem12  10698  trclublem  15115  relexpcnv  15155  relexpnnrn  15165  invf  17904  cicsym  17940  cnvtsr  18723  znleval  21821  ordtbas2  23470  ordtcnv  23480  ordtrest2  23483  cnconn  23701  tgqtop  23992  adj1o  32429  fcoinver  33131  fresf1o  33158  fcnvgreu  33199  dfcnv2  33202  preiman0  33236  gsumhashmul  33561  cycpmfvlem  33606  cycpmfv1  33607  cycpmfv2  33608  cycpmfv3  33609  cycpmrn  33637  cnvordtrestixx  34478  xrge0iifhmeo  34501  mbfmcst  34825  0rrv  35017  elrn3  36448  dfrn6  39160  cnvresrn  39200  dmxrn  39239  dmcoss2  39396  cnvrcl0  44569  conrel2d  44608  relexpaddss  44662  rntrclfvRP  44675  ntrneifv2  45024
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