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Definition df-0o 28536
 Description: Define the zero operator between two normed complex vector spaces. (Contributed by NM, 28-Nov-2007.) (New usage is discouraged.)
Assertion
Ref Expression
df-0o 0op = (𝑢 ∈ NrmCVec, 𝑤 ∈ NrmCVec ↦ ((BaseSet‘𝑢) × {(0vec𝑤)}))
Distinct variable group:   𝑤,𝑢

Detailed syntax breakdown of Definition df-0o
StepHypRef Expression
1 c0o 28532 . 2 class 0op
2 vu . . 3 setvar 𝑢
3 vw . . 3 setvar 𝑤
4 cnv 28373 . . 3 class NrmCVec
52cv 1537 . . . . 5 class 𝑢
6 cba 28375 . . . . 5 class BaseSet
75, 6cfv 6344 . . . 4 class (BaseSet‘𝑢)
83cv 1537 . . . . . 6 class 𝑤
9 cn0v 28377 . . . . . 6 class 0vec
108, 9cfv 6344 . . . . 5 class (0vec𝑤)
1110csn 4551 . . . 4 class {(0vec𝑤)}
127, 11cxp 5541 . . 3 class ((BaseSet‘𝑢) × {(0vec𝑤)})
132, 3, 4, 4, 12cmpo 7152 . 2 class (𝑢 ∈ NrmCVec, 𝑤 ∈ NrmCVec ↦ ((BaseSet‘𝑢) × {(0vec𝑤)}))
141, 13wceq 1538 1 wff 0op = (𝑢 ∈ NrmCVec, 𝑤 ∈ NrmCVec ↦ ((BaseSet‘𝑢) × {(0vec𝑤)}))
 Colors of variables: wff setvar class This definition is referenced by:  0ofval  28576
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