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Mirrors > Home > MPE Home > Th. List > df-dm | Unicode version |
Description: Define the domain of a
class. Definition 3 of [Suppes] p. 59. For
example, = { <. 2 , 6 >. , <. 3 , 9 >. } -> dom = { 2 , 3 }
(ex-dm 25160). Another example is the domain of the
complex arctangent,
(for
proof see atandm 23207). Contrast with range (defined in df-rn 5015). For
alternate definitions see dfdm2 5544, dfdm3 5195, and dfdm4 5200. The
notation "dom " is used by
Enderton; other authors sometimes use
script D. (Contributed by NM, 1-Aug-1994.) |
Ref | Expression |
---|---|
df-dm |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 | |
2 | 1 | cdm 5004 | . 2 |
3 | vx | . . . . . 6 | |
4 | 3 | cv 1394 | . . . . 5 |
5 | vy | . . . . . 6 | |
6 | 5 | cv 1394 | . . . . 5 |
7 | 4, 6, 1 | wbr 4452 | . . . 4 |
8 | 7, 5 | wex 1612 | . . 3 |
9 | 8, 3 | cab 2442 | . 2 |
10 | 2, 9 | wceq 1395 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: dfdm3 5195 dfrn2 5196 dfdm4 5200 dfdmf 5201 eldmg 5203 dmun 5214 dm0rn0 5224 nfdm 5249 fliftf 6213 opabdm 27464 domep 29225 |
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