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Definition df-cbn 28554
Description: Define the class of all complex Banach spaces. (Contributed by NM, 5-Dec-2006.) Use df-bn 23854 instead. (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 28553 . 2 class CBan
2 vu . . . . . 6 setvar 𝑢
32cv 1529 . . . . 5 class 𝑢
4 cims 28282 . . . . 5 class IndMet
53, 4cfv 6351 . . . 4 class (IndMet‘𝑢)
6 cba 28277 . . . . . 6 class BaseSet
73, 6cfv 6351 . . . . 5 class (BaseSet‘𝑢)
8 ccmet 23772 . . . . 5 class CMet
97, 8cfv 6351 . . . 4 class (CMet‘(BaseSet‘𝑢))
105, 9wcel 2107 . . 3 wff (IndMet‘𝑢) ∈ (CMet‘(BaseSet‘𝑢))
11 cnv 28275 . . 3 class NrmCVec
1210, 2, 11crab 3146 . 2 class {𝑢 ∈ NrmCVec ∣ (IndMet‘𝑢) ∈ (CMet‘(BaseSet‘𝑢))}
131, 12wceq 1530 1 wff CBan = {𝑢 ∈ NrmCVec ∣ (IndMet‘𝑢) ∈ (CMet‘(BaseSet‘𝑢))}
Colors of variables: wff setvar class
This definition is referenced by:  iscbn  28555
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