Description: Every complex Banach space is a normed complex vector space. (Contributed by NM, 17-Mar-2007) Use bnnvc instead. (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | bnnv | |- ( U e. CBan -> U e. NrmCVec ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid | |- ( BaseSet ` U ) = ( BaseSet ` U ) |
|
2 | eqid | |- ( IndMet ` U ) = ( IndMet ` U ) |
|
3 | 1 2 | iscbn | |- ( U e. CBan <-> ( U e. NrmCVec /\ ( IndMet ` U ) e. ( CMet ` ( BaseSet ` U ) ) ) ) |
4 | 3 | simplbi | |- ( U e. CBan -> U e. NrmCVec ) |