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	$$⊢\mathrm{dom}A=\left\{x|\exists yxAy\right\}$$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cA	$$classA$$
1	0	cdm	$$class\mathrm{dom}A$$
2		vx	$$setvarx$$
3		vy	$$setvary$$
4	2	cv	$$setvarx$$
5	3	cv	$$setvary$$
6	4 5 0	wbr	$$wffxAy$$
7	6 3	wex	$$wff\exists yxAy$$
8	7 2	cab	$$class\left\{x|\exists yxAy\right\}$$
9	1 8	wceq	$$wff\mathrm{dom}A=\left\{x|\exists yxAy\right\}$$