Definition df-dm 4784

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 4785). For alternate definitions see dfdm2 5322, dfdm3 4967, and dfdm4 4973. 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 | E. y x A y }

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 4774	. 2 class dom A
3		vx	. . . . . 6 setvar x
4	3	cv 1401	. . . . 5 class x
5		vy	. . . . . 6 setvar y
6	5	cv 1401	. . . . 5 class y
7	4, 6, 1	wbr 4130	. . . 4 wff x A y
8	7, 5	wex 1545	. . 3 wff E. y x A y
9	8, 3	cab 2224	. 2 class { x | E. y x A y }
10	2, 9	wceq 1402	1 wff dom A = { x | E. y x A y }

This definition is used by:  dfdm3  4967  dfrn2  4968  dfdm4  4973  dfdmf  4974  eldmg  4976  dmun  4988  dm0rn0  4998  dmmrnm  5001  nfdm  5026  fliftf  6005