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Definition df-evl 20836
 Description: A simplification of evalSub when the evaluation ring is the same as the coefficient ring. (Contributed by Stefan O'Rear, 19-Mar-2015.)
Assertion
Ref Expression
df-evl eval = (𝑖 ∈ V, 𝑟 ∈ V ↦ ((𝑖 evalSub 𝑟)‘(Base‘𝑟)))
Distinct variable group:   𝑖,𝑟

Detailed syntax breakdown of Definition df-evl
StepHypRef Expression
1 cevl 20834 . 2 class eval
2 vi . . 3 setvar 𝑖
3 vr . . 3 setvar 𝑟
4 cvv 3409 . . 3 class V
53cv 1537 . . . . 5 class 𝑟
6 cbs 16541 . . . . 5 class Base
75, 6cfv 6335 . . . 4 class (Base‘𝑟)
82cv 1537 . . . . 5 class 𝑖
9 ces 20833 . . . . 5 class evalSub
108, 5, 9co 7150 . . . 4 class (𝑖 evalSub 𝑟)
117, 10cfv 6335 . . 3 class ((𝑖 evalSub 𝑟)‘(Base‘𝑟))
122, 3, 4, 4, 11cmpo 7152 . 2 class (𝑖 ∈ V, 𝑟 ∈ V ↦ ((𝑖 evalSub 𝑟)‘(Base‘𝑟)))
131, 12wceq 1538 1 wff eval = (𝑖 ∈ V, 𝑟 ∈ V ↦ ((𝑖 evalSub 𝑟)‘(Base‘𝑟)))
 Colors of variables: wff setvar class This definition is referenced by:  evlval  20858  evl1fval  21047  mzpmfp  40061
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