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Definition df-dm 4699
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 20802). 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 20167). Contrast with range (defined in df-rn 4700). For alternate definitions see dfdm2 5203, dfdm3 4867, and dfdm4 4872. 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 4689 . 2  class  dom  A
3 vx . . . . . 6  set  x
43cv 1623 . . . . 5  class  x
5 vy . . . . . 6  set  y
65cv 1623 . . . . 5  class  y
74, 6, 1wbr 4025 . . . 4  wff  x A y
87, 5wex 1529 . . 3  wff  E. y  x A y
98, 3cab 2271 . 2  class  { x  |  E. y  x A y }
102, 9wceq 1624 1  wff  dom  A  =  { x  |  E. y  x A y }
Colors of variables: wff set class
This definition is referenced by:  dfdm3  4867  dfrn2  4868  dfdm4  4872  dfdmf  4873  eldmg  4874  dmun  4885  dm0rn0  4895  nfdm  4920  fliftf  5776  domep  23551
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