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Definition df-ims 28387
 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 28377 . 2 class IndMet
2 vu . . 3 setvar 𝑢
3 cnv 28370 . . 3 class NrmCVec
42cv 1537 . . . . 5 class 𝑢
5 cnmcv 28376 . . . . 5 class normCV
64, 5cfv 6328 . . . 4 class (normCV𝑢)
7 cnsb 28375 . . . . 5 class 𝑣
84, 7cfv 6328 . . . 4 class ( −𝑣𝑢)
96, 8ccom 5527 . . 3 class ((normCV𝑢) ∘ ( −𝑣𝑢))
102, 3, 9cmpt 5113 . 2 class (𝑢 ∈ NrmCVec ↦ ((normCV𝑢) ∘ ( −𝑣𝑢)))
111, 10wceq 1538 1 wff IndMet = (𝑢 ∈ NrmCVec ↦ ((normCV𝑢) ∘ ( −𝑣𝑢)))
 Colors of variables: wff setvar class This definition is referenced by:  imsval  28471
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