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Definition df-cbn 28069
Description: Define the class of all complex Banach spaces. (Contributed by NM, 5-Dec-2006.) (New usage is discouraged.)
Assertion
Ref Expression
df-cbn CBan = {𝑢 ∈ NrmCVec ∣ (IndMet‘𝑢) ∈ (CMet‘(BaseSet‘𝑢))}

Detailed syntax breakdown of Definition df-cbn
StepHypRef Expression
1 ccbn 28068 . 2 class CBan
2 vu . . . . . 6 setvar 𝑢
32cv 1636 . . . . 5 class 𝑢
4 cims 27796 . . . . 5 class IndMet
53, 4cfv 6110 . . . 4 class (IndMet‘𝑢)
6 cba 27791 . . . . . 6 class BaseSet
73, 6cfv 6110 . . . . 5 class (BaseSet‘𝑢)
8 cms 23285 . . . . 5 class CMet
97, 8cfv 6110 . . . 4 class (CMet‘(BaseSet‘𝑢))
105, 9wcel 2157 . . 3 wff (IndMet‘𝑢) ∈ (CMet‘(BaseSet‘𝑢))
11 cnv 27789 . . 3 class NrmCVec
1210, 2, 11crab 3111 . 2 class {𝑢 ∈ NrmCVec ∣ (IndMet‘𝑢) ∈ (CMet‘(BaseSet‘𝑢))}
131, 12wceq 1637 1 wff CBan = {𝑢 ∈ NrmCVec ∣ (IndMet‘𝑢) ∈ (CMet‘(BaseSet‘𝑢))}
Colors of variables: wff setvar class
This definition is referenced by:  iscbn  28070
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