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Mirrors > Home > ILE Home > Th. List > df-dm | GIF version |
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 4299). For alternate definitions see dfdm2 4795, dfdm3 4465, and dfdm4 4470. The notation "dom " is used by Enderton; other authors sometimes use script D. (Contributed by NM, 1-Aug-1994.) |
Ref | Expression |
---|---|
df-dm | ⊢ dom A = {x ∣ ∃y xAy} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cA | . . 3 class A | |
2 | 1 | cdm 4288 | . 2 class dom A |
3 | vx | . . . . . 6 setvar x | |
4 | 3 | cv 1241 | . . . . 5 class x |
5 | vy | . . . . . 6 setvar y | |
6 | 5 | cv 1241 | . . . . 5 class y |
7 | 4, 6, 1 | wbr 3755 | . . . 4 wff xAy |
8 | 7, 5 | wex 1378 | . . 3 wff ∃y xAy |
9 | 8, 3 | cab 2023 | . 2 class {x ∣ ∃y xAy} |
10 | 2, 9 | wceq 1242 | 1 wff dom A = {x ∣ ∃y xAy} |
Colors of variables: wff set class |
This definition is referenced by: dfdm3 4465 dfrn2 4466 dfdm4 4470 dfdmf 4471 eldmg 4473 dmun 4485 dm0rn0 4495 dmmrnm 4497 nfdm 4521 fliftf 5382 |
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