This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: The vector addition operation of a normed complex vector space is a
group. (Contributed by NM, 15-Feb-2008)
(New usage is discouraged.)
|
|
Ref |
Expression |
|
Hypothesis |
nvabl.1 |
⊢ 𝐺 = ( +𝑣 ‘ 𝑈 ) |
|
Assertion |
nvgrp |
⊢ ( 𝑈 ∈ NrmCVec → 𝐺 ∈ GrpOp ) |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
nvabl.1 |
⊢ 𝐺 = ( +𝑣 ‘ 𝑈 ) |
| 2 |
1
|
nvablo |
⊢ ( 𝑈 ∈ NrmCVec → 𝐺 ∈ AbelOp ) |
| 3 |
|
ablogrpo |
⊢ ( 𝐺 ∈ AbelOp → 𝐺 ∈ GrpOp ) |
| 4 |
2 3
|
syl |
⊢ ( 𝑈 ∈ NrmCVec → 𝐺 ∈ GrpOp ) |