Definition df-ba 30116

Description: Define the base set of a normed complex vector space. (Contributed by NM, 23-Apr-2007.) (New usage is discouraged.)

Assertion

Ref	Expression
df-ba	⊢ BaseSet = (𝑥 ∈ V ↦ ran ( +𝑣 ‘𝑥))

Detailed syntax breakdown of Definition df-ba

Step	Hyp	Ref	Expression
1		cba 30106	. 2 class BaseSet
2		vx	. . 3 setvar 𝑥
3		cvv 3472	. . 3 class V
4	2	cv 1538	. . . . 5 class 𝑥
5		cpv 30105	. . . . 5 class +𝑣
6	4, 5	cfv 6542	. . . 4 class ( +𝑣 ‘𝑥)
7	6	crn 5676	. . 3 class ran ( +𝑣 ‘𝑥)
8	2, 3, 7	cmpt 5230	. 2 class (𝑥 ∈ V ↦ ran ( +𝑣 ‘𝑥))
9	1, 8	wceq 1539	1 wff BaseSet = (𝑥 ∈ V ↦ ran ( +𝑣 ‘𝑥))

This definition is referenced by:  bafval  30124