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Definition df-dm 4851
Description: Define the domain of a class. Definition 3 of [Suppes] p. 59. For example,  F  =  { <. 2 ,  6 >. ,  <. 3 ,  9
>. }  ->  dom  F  =  { 2 ,  3 } (ex-dm 21704). Another example is the domain of the complex arctangent,  ( A  e. 
dom arctan 
<->  ( A  e.  CC  /\  A  =/=  -u _i  /\  A  =/=  _i ) ) (for proof see atandm 20673). Contrast with range (defined in df-rn 4852). For alternate definitions see dfdm2 5364, dfdm3 5021, and dfdm4 5026. 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 4841 . 2  class  dom  A
3 vx . . . . . 6  set  x
43cv 1648 . . . . 5  class  x
5 vy . . . . . 6  set  y
65cv 1648 . . . . 5  class  y
74, 6, 1wbr 4176 . . . 4  wff  x A y
87, 5wex 1547 . . 3  wff  E. y  x A y
98, 3cab 2394 . 2  class  { x  |  E. y  x A y }
102, 9wceq 1649 1  wff  dom  A  =  { x  |  E. y  x A y }
Colors of variables: wff set class
This definition is referenced by:  dfdm3  5021  dfrn2  5022  dfdm4  5026  dfdmf  5027  eldmg  5028  dmun  5039  dm0rn0  5049  nfdm  5074  fliftf  6000  domep  25367
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