MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-ba Structured version   Visualization version   GIF version

Definition df-ba 27773
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 ( +𝑣𝑥))

Detailed syntax breakdown of Definition df-ba
StepHypRef Expression
1 cba 27763 . 2 class BaseSet
2 vx . . 3 setvar 𝑥
3 cvv 3387 . . 3 class V
42cv 1636 . . . . 5 class 𝑥
5 cpv 27762 . . . . 5 class +𝑣
64, 5cfv 6095 . . . 4 class ( +𝑣𝑥)
76crn 5306 . . 3 class ran ( +𝑣𝑥)
82, 3, 7cmpt 4916 . 2 class (𝑥 ∈ V ↦ ran ( +𝑣𝑥))
91, 8wceq 1637 1 wff BaseSet = (𝑥 ∈ V ↦ ran ( +𝑣𝑥))
Colors of variables: wff setvar class
This definition is referenced by:  bafval  27781
  Copyright terms: Public domain W3C validator