Definition df-dm 4786

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 4787). For alternate definitions see dfdm2 5325, dfdm3 4969, and dfdm4 4975. 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 4776	. 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 4131	. . . 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  4969  dfrn2  4970  dfdm4  4975  dfdmf  4976  eldmg  4978  dmun  4990  dm0rn0  5000  dmmrnm  5003  nfdm  5028  fliftf  6008