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Definition df-mulv 41103
 Description: Define the operation of scalar multiplication. (Contributed by Andrew Salmon, 27-Jan-2012.)
Assertion
Ref Expression
df-mulv .𝑣 = (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑣 ∈ ℝ ↦ (𝑥 · (𝑦𝑣))))
Distinct variable group:   𝑥,𝑣,𝑦

Detailed syntax breakdown of Definition df-mulv
StepHypRef Expression
1 ctimesr 41097 . 2 class .𝑣
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cvv 3469 . . 3 class V
5 vv . . . 4 setvar 𝑣
6 cr 10525 . . . 4 class
72cv 1537 . . . . 5 class 𝑥
85cv 1537 . . . . . 6 class 𝑣
93cv 1537 . . . . . 6 class 𝑦
108, 9cfv 6334 . . . . 5 class (𝑦𝑣)
11 cmul 10531 . . . . 5 class ·
127, 10, 11co 7140 . . . 4 class (𝑥 · (𝑦𝑣))
135, 6, 12cmpt 5122 . . 3 class (𝑣 ∈ ℝ ↦ (𝑥 · (𝑦𝑣)))
142, 3, 4, 4, 13cmpo 7142 . 2 class (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑣 ∈ ℝ ↦ (𝑥 · (𝑦𝑣))))
151, 14wceq 1538 1 wff .𝑣 = (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑣 ∈ ℝ ↦ (𝑥 · (𝑦𝑣))))
 Colors of variables: wff setvar class This definition is referenced by:  mulvval  41106
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