Description: The vector addition operation of a normed complex vector space is an Abelian group. (Contributed by NM, 15-Feb-2008) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | nvabl.1 | |- G = ( +v ` U ) |
|
| Assertion | nvablo | |- ( U e. NrmCVec -> G e. AbelOp ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nvabl.1 | |- G = ( +v ` U ) |
|
| 2 | eqid | |- ( 1st ` U ) = ( 1st ` U ) |
|
| 3 | 2 | nvvc | |- ( U e. NrmCVec -> ( 1st ` U ) e. CVecOLD ) |
| 4 | 1 | vafval | |- G = ( 1st ` ( 1st ` U ) ) |
| 5 | 4 | vcablo | |- ( ( 1st ` U ) e. CVecOLD -> G e. AbelOp ) |
| 6 | 3 5 | syl | |- ( U e. NrmCVec -> G e. AbelOp ) |