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Definition df-evl 19488
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 19486 . 2 class eval
2 vi . . 3 setvar 𝑖
3 vr . . 3 setvar 𝑟
4 cvv 3195 . . 3 class V
53cv 1480 . . . . 5 class 𝑟
6 cbs 15838 . . . . 5 class Base
75, 6cfv 5876 . . . 4 class (Base‘𝑟)
82cv 1480 . . . . 5 class 𝑖
9 ces 19485 . . . . 5 class evalSub
108, 5, 9co 6635 . . . 4 class (𝑖 evalSub 𝑟)
117, 10cfv 5876 . . 3 class ((𝑖 evalSub 𝑟)‘(Base‘𝑟))
122, 3, 4, 4, 11cmpt2 6637 . 2 class (𝑖 ∈ V, 𝑟 ∈ V ↦ ((𝑖 evalSub 𝑟)‘(Base‘𝑟)))
131, 12wceq 1481 1 wff eval = (𝑖 ∈ V, 𝑟 ∈ V ↦ ((𝑖 evalSub 𝑟)‘(Base‘𝑟)))
Colors of variables: wff setvar class
This definition is referenced by:  evlval  19505  evl1fval  19673  mzpmfp  37129
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