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Definition df-evl1 17944
Description: Define the evaluation map for the univariate polynomial algebra. The function makes sense when is a ring, and is the set of polynomials in . This function maps an element of the formal polynomial algebra (with coefficients in ) to a function from assignments to the variable from into an element of formed by evaluating the polynomial with the given assignment. (Contributed by Mario Carneiro, 12-Jun-2015.)
Assertion
Ref Expression
df-evl1
Distinct variable group:   , , ,

Detailed syntax breakdown of Definition df-evl1
StepHypRef Expression
1 ce1 17942 . 2
2 vr . . 3
3 cvv 3081 . . 3
4 vb . . . 4
52cv 1369 . . . . 5
6 cbs 14332 . . . . 5
75, 6cfv 5537 . . . 4
8 vx . . . . . 6
94cv 1369 . . . . . . 7
10 c1o 7047 . . . . . . . 8
11 cmap 7348 . . . . . . . 8
129, 10, 11co 6222 . . . . . . 7
139, 12, 11co 6222 . . . . . 6
148cv 1369 . . . . . . 7
15 vy . . . . . . . 8
1615cv 1369 . . . . . . . . . 10
1716csn 3993 . . . . . . . . 9
1810, 17cxp 4955 . . . . . . . 8
1915, 9, 18cmpt 4467 . . . . . . 7
2014, 19ccom 4961 . . . . . 6
218, 13, 20cmpt 4467 . . . . 5
22 cevl 17764 . . . . . 6
2310, 5, 22co 6222 . . . . 5
2421, 23ccom 4961 . . . 4
254, 7, 24csb 3401 . . 3
262, 3, 25cmpt 4467 . 2
271, 26wceq 1370 1
Colors of variables: wff setvar class
This definition is referenced by:  evl1fval  17955
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