Definition df-dm 5124

Description: Define the domain of a class. Definition 3 of [Suppes] p. 59. For example, F = { <. 2 , 6 >. , <. 3 , 9 >. } -> dom F = { 2 , 3 } (ex-dm 27296). Another example is the domain of the complex arctangent, ( A e. dom arctan <-> ( A e. CC /\ A =/= -u _i /\ A =/= _i ) ) (for proof see atandm 24603). Contrast with range (defined in df-rn 5125). For alternate definitions see dfdm2 5667, dfdm3 5310, and dfdm4 5316. 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 5114	. 2 class dom A
3		vx	. . . . . 6 setvar x
4	3	cv 1482	. . . . 5 class x
5		vy	. . . . . 6 setvar y
6	5	cv 1482	. . . . 5 class y
7	4, 6, 1	wbr 4653	. . . 4 wff x A y
8	7, 5	wex 1704	. . 3 wff E. y x A y
9	8, 3	cab 2608	. 2 class { x | E. y x A y }
10	2, 9	wceq 1483	1 wff dom A = { x | E. y x A y }

This definition is referenced by:  dfdm3  5310  dfrn2  5311  dfdm4  5316  dfdmf  5317  eldmg  5319  dmun  5331  dm0rn0  5342  nfdm  5367  fliftf  6565  opabdm  29423  domep  31698