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Definition df-dm 4423
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 4424). For alternate definitions see dfdm2 4933, dfdm3 4593, and dfdm4 4598. 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 ∣ ∃𝑦 𝑥𝐴𝑦}
Distinct variable group:   𝑥,𝑦,𝐴

Detailed syntax breakdown of Definition df-dm
StepHypRef Expression
1 cA . . 3 class 𝐴
21cdm 4413 . 2 class dom 𝐴
3 vx . . . . . 6 setvar 𝑥
43cv 1286 . . . . 5 class 𝑥
5 vy . . . . . 6 setvar 𝑦
65cv 1286 . . . . 5 class 𝑦
74, 6, 1wbr 3822 . . . 4 wff 𝑥𝐴𝑦
87, 5wex 1424 . . 3 wff 𝑦 𝑥𝐴𝑦
98, 3cab 2071 . 2 class {𝑥 ∣ ∃𝑦 𝑥𝐴𝑦}
102, 9wceq 1287 1 wff dom 𝐴 = {𝑥 ∣ ∃𝑦 𝑥𝐴𝑦}
Colors of variables: wff set class
This definition is referenced by:  dfdm3  4593  dfrn2  4594  dfdm4  4598  dfdmf  4599  eldmg  4601  dmun  4613  dm0rn0  4623  dmmrnm  4625  nfdm  4649  fliftf  5541
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