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Definition df-ims 27584
Description: Define the induced metric on a normed complex vector space. (Contributed by NM, 11-Sep-2007.) (New usage is discouraged.)
Assertion
Ref Expression
df-ims IndMet = (𝑢 ∈ NrmCVec ↦ ((normCV𝑢) ∘ ( −𝑣𝑢)))

Detailed syntax breakdown of Definition df-ims
StepHypRef Expression
1 cims 27574 . 2 class IndMet
2 vu . . 3 setvar 𝑢
3 cnv 27567 . . 3 class NrmCVec
42cv 1522 . . . . 5 class 𝑢
5 cnmcv 27573 . . . . 5 class normCV
64, 5cfv 5926 . . . 4 class (normCV𝑢)
7 cnsb 27572 . . . . 5 class 𝑣
84, 7cfv 5926 . . . 4 class ( −𝑣𝑢)
96, 8ccom 5147 . . 3 class ((normCV𝑢) ∘ ( −𝑣𝑢))
102, 3, 9cmpt 4762 . 2 class (𝑢 ∈ NrmCVec ↦ ((normCV𝑢) ∘ ( −𝑣𝑢)))
111, 10wceq 1523 1 wff IndMet = (𝑢 ∈ NrmCVec ↦ ((normCV𝑢) ∘ ( −𝑣𝑢)))
Colors of variables: wff setvar class
This definition is referenced by:  imsval  27668
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