Definition df-dm 4278

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 4279). For alternate definitions see dfdm2 4775, dfdm3 4445, and dfdm4 4450. 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

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2	1	cdm 4268	. 2 class dom A
3		vx	. . . . . 6 setvar x
4	3	cv 1225	. . . . 5 class x
5		vy	. . . . . 6 setvar y
6	5	cv 1225	. . . . 5 class y
7	4, 6, 1	wbr 3734	. . . 4 wff xAy
8	7, 5	wex 1358	. . 3 wff ∃y xAy
9	8, 3	cab 2004	. 2 class {x ∣ ∃y xAy}
10	2, 9	wceq 1226	1 wff dom A = {x ∣ ∃y xAy}

This definition is referenced by:  dfdm3  4445  dfrn2  4446  dfdm4  4450  dfdmf  4451  eldmg  4453  dmun  4465  dm0rn0  4475  dmmrnm  4477  nfdm  4501  fliftf  5360