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Definition df-dm 4409
Description: Define the domain of a class. Definition 3 of [Suppes] p. 59. For example, F = {  <. 2 , 6  >.,  <. 3 , 9  >. }  -> dom F = { 2 , 3 } . Contrast with range (defined in df-rn 4410). For alternate definitions see dfdm2 4917, dfdm3 4579, and dfdm4 4584. The notation " dom " is used by Enderton; other authors sometimes use script D. (Contributed by NM, 1-Aug-1994.)
Assertion
Ref Expression
df-dm  |-  dom  A  =  { x  |  E. y  x A y }
Distinct variable group:    x, y, A

Detailed syntax breakdown of Definition df-dm
StepHypRef Expression
1 cA . . 3  class  A
21cdm 4399 . 2  class  dom  A
3 vx . . . . . 6  setvar  x
43cv 1284 . . . . 5  class  x
5 vy . . . . . 6  setvar  y
65cv 1284 . . . . 5  class  y
74, 6, 1wbr 3811 . . . 4  wff  x A y
87, 5wex 1422 . . 3  wff  E. y  x A y
98, 3cab 2069 . 2  class  { x  |  E. y  x A y }
102, 9wceq 1285 1  wff  dom  A  =  { x  |  E. y  x A y }
Colors of variables: wff set class
This definition is referenced by:  dfdm3  4579  dfrn2  4580  dfdm4  4584  dfdmf  4585  eldmg  4587  dmun  4599  dm0rn0  4609  dmmrnm  4611  nfdm  4635  fliftf  5516
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