Definition df-dm

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 ). Another example is the domain of the complex arctangent, ( A e. dom arctan <-> ( A e. CC /\ A =/= -ui /\ A =/= i ) ) (for proof see atandm ). Contrast with range (defined in df-rn ). For alternate definitions see dfdm2 , dfdm3 , and dfdm4 . The notation " dom " is used by Enderton; other authors sometimes use script D. (Contributed by NM, 1-Aug-1994)

	Ref	Expression
Assertion	df-dm	|- dom A = { x | E. y x A y }

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cA	|- A
1	0	cdm	|- dom A
2		vx	|- x
3		vy	|- y
4	2	cv	|- x
5	3	cv	|- y
6	4 5 0	wbr	|- x A y
7	6 3	wex	|- E. y x A y
8	7 2	cab	|- { x | E. y x A y }
9	1 8	wceq	|- dom A = { x | E. y x A y }