This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Definition df-ba
Description: Define the base set of a normed complex vector space. (Contributed by NM, 23-Apr-2007) (New usage is discouraged.)
|
|
Ref |
Expression |
|
Assertion |
df-ba |
⊢ BaseSet = ( 𝑥 ∈ V ↦ ran ( +𝑣 ‘ 𝑥 ) ) |
Detailed syntax breakdown
| Step |
Hyp |
Ref |
Expression |
| 0 |
|
cba |
⊢ BaseSet |
| 1 |
|
vx |
⊢ 𝑥 |
| 2 |
|
cvv |
⊢ V |
| 3 |
|
cpv |
⊢ +𝑣 |
| 4 |
1
|
cv |
⊢ 𝑥 |
| 5 |
4 3
|
cfv |
⊢ ( +𝑣 ‘ 𝑥 ) |
| 6 |
5
|
crn |
⊢ ran ( +𝑣 ‘ 𝑥 ) |
| 7 |
1 2 6
|
cmpt |
⊢ ( 𝑥 ∈ V ↦ ran ( +𝑣 ‘ 𝑥 ) ) |
| 8 |
0 7
|
wceq |
⊢ BaseSet = ( 𝑥 ∈ V ↦ ran ( +𝑣 ‘ 𝑥 ) ) |