Metamath Proof Explorer

Definition df-dm

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 ). Another example is the domain of the complex arctangent, ( A e. dom arctan <-> ( A e. CC /\ A =/= -ui /\ A =/= i ) ) (for proof see atandm ). Contrast with range (defined in df-rn ). For alternate definitions see dfdm2 , dfdm3 , and dfdm4 . The notation " dom " is used by Enderton; other authors sometimes use script D. (Contributed by NM, 1-Aug-1994)

|- dom A = { x | E. y x A y }

 |-  A

 |-  dom A

 |-  x

 |-  y

 |-  x

 |-  y

 |-  x A y

 |-  E. y x A y

 |-  { x | E. y x A y }

 |-  dom A = { x | E. y x A y }