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Definition df-dm 4381
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 4382). For alternate definitions see dfdm2 4882, dfdm3 4550, and dfdm4 4555. 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 4371 . 2 class dom 𝐴
3 vx . . . . . 6 setvar 𝑥
43cv 1284 . . . . 5 class 𝑥
5 vy . . . . . 6 setvar 𝑦
65cv 1284 . . . . 5 class 𝑦
74, 6, 1wbr 3793 . . . 4 wff 𝑥𝐴𝑦
87, 5wex 1422 . . 3 wff 𝑦 𝑥𝐴𝑦
98, 3cab 2068 . 2 class {𝑥 ∣ ∃𝑦 𝑥𝐴𝑦}
102, 9wceq 1285 1 wff dom 𝐴 = {𝑥 ∣ ∃𝑦 𝑥𝐴𝑦}
Colors of variables: wff set class
This definition is referenced by:  dfdm3  4550  dfrn2  4551  dfdm4  4555  dfdmf  4556  eldmg  4558  dmun  4570  dm0rn0  4580  dmmrnm  4582  nfdm  4606  fliftf  5470
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