Definition df-dm 4270

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 4271). For alternate definitions see dfdm2 4767, dfdm3 4437, and dfdm4 4442. 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 4260	. 2 class dom A
3		vx	. . . . . 6 setvar x
4	3	cv 1222	. . . . 5 class x
5		vy	. . . . . 6 setvar y
6	5	cv 1222	. . . . 5 class y
7	4, 6, 1	wbr 3727	. . . 4 wff xAy
8	7, 5	wex 1354	. . 3 wff ∃y xAy
9	8, 3	cab 1999	. 2 class {x ∣ ∃y xAy}
10	2, 9	wceq 1223	1 wff dom A = {x ∣ ∃y xAy}

This definition is referenced by:  dfdm3  4437  dfrn2  4438  dfdm4  4442  dfdmf  4443  eldmg  4445  dmun  4457  dm0rn0  4467  dmmrnm  4469  nfdm  4493  fliftf  5352