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Mirrors > Home > MPE Home > Th. List > df-ba | Structured version Visualization version GIF version |
Description: Define the base set of a normed complex vector space. (Contributed by NM, 23-Apr-2007.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-ba | ⊢ BaseSet = (𝑥 ∈ V ↦ ran ( +𝑣 ‘𝑥)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cba 28667 | . 2 class BaseSet | |
2 | vx | . . 3 setvar 𝑥 | |
3 | cvv 3408 | . . 3 class V | |
4 | 2 | cv 1542 | . . . . 5 class 𝑥 |
5 | cpv 28666 | . . . . 5 class +𝑣 | |
6 | 4, 5 | cfv 6380 | . . . 4 class ( +𝑣 ‘𝑥) |
7 | 6 | crn 5552 | . . 3 class ran ( +𝑣 ‘𝑥) |
8 | 2, 3, 7 | cmpt 5135 | . 2 class (𝑥 ∈ V ↦ ran ( +𝑣 ‘𝑥)) |
9 | 1, 8 | wceq 1543 | 1 wff BaseSet = (𝑥 ∈ V ↦ ran ( +𝑣 ‘𝑥)) |
Colors of variables: wff setvar class |
This definition is referenced by: bafval 28685 |
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