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Definition df-dm 4556
 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 4557). For alternate definitions see dfdm2 5080, dfdm3 4733, and dfdm4 4738. 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 4546 . 2 class dom 𝐴
3 vx . . . . . 6 setvar 𝑥
43cv 1331 . . . . 5 class 𝑥
5 vy . . . . . 6 setvar 𝑦
65cv 1331 . . . . 5 class 𝑦
74, 6, 1wbr 3936 . . . 4 wff 𝑥𝐴𝑦
87, 5wex 1469 . . 3 wff 𝑦 𝑥𝐴𝑦
98, 3cab 2126 . 2 class {𝑥 ∣ ∃𝑦 𝑥𝐴𝑦}
102, 9wceq 1332 1 wff dom 𝐴 = {𝑥 ∣ ∃𝑦 𝑥𝐴𝑦}
 Colors of variables: wff set class This definition is referenced by:  dfdm3  4733  dfrn2  4734  dfdm4  4738  dfdmf  4739  eldmg  4741  dmun  4753  dm0rn0  4763  dmmrnm  4765  nfdm  4790  fliftf  5707
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