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Definition df-mulv 38495
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 38489 . 2 class .𝑣
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cvv 3198 . . 3 class V
5 vv . . . 4 setvar 𝑣
6 cr 9932 . . . 4 class
72cv 1481 . . . . 5 class 𝑥
85cv 1481 . . . . . 6 class 𝑣
93cv 1481 . . . . . 6 class 𝑦
108, 9cfv 5886 . . . . 5 class (𝑦𝑣)
11 cmul 9938 . . . . 5 class ·
127, 10, 11co 6647 . . . 4 class (𝑥 · (𝑦𝑣))
135, 6, 12cmpt 4727 . . 3 class (𝑣 ∈ ℝ ↦ (𝑥 · (𝑦𝑣)))
142, 3, 4, 4, 13cmpt2 6649 . 2 class (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑣 ∈ ℝ ↦ (𝑥 · (𝑦𝑣))))
151, 14wceq 1482 1 wff .𝑣 = (𝑥 ∈ V, 𝑦 ∈ V ↦ (𝑣 ∈ ℝ ↦ (𝑥 · (𝑦𝑣))))
Colors of variables: wff setvar class
This definition is referenced by:  mulvval  38498
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