Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-evl1 Structured version   Unicode version

Definition df-evl1 16572
 Description: Define the evaluation map for the univariate polynomial algebra. The function eval1 makes sense when is a ring, and is the set of polynomials in Poly1. 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 eval1 eval
Distinct variable group:   ,,,

Detailed syntax breakdown of Definition df-evl1
StepHypRef Expression
1 ce1 16565 . 2 eval1
2 vr . . 3
3 cvv 2948 . . 3
4 vb . . . 4
52cv 1651 . . . . 5
6 cbs 13461 . . . . 5
75, 6cfv 5446 . . . 4
8 vx . . . . . 6
94cv 1651 . . . . . . 7
10 c1o 6709 . . . . . . . 8
11 cmap 7010 . . . . . . . 8
129, 10, 11co 6073 . . . . . . 7
139, 12, 11co 6073 . . . . . 6
148cv 1651 . . . . . . 7
15 vy . . . . . . . 8
1615cv 1651 . . . . . . . . . 10
1716csn 3806 . . . . . . . . 9
1810, 17cxp 4868 . . . . . . . 8
1915, 9, 18cmpt 4258 . . . . . . 7
2014, 19ccom 4874 . . . . . 6
218, 13, 20cmpt 4258 . . . . 5
22 cevl 16402 . . . . . 6 eval
2310, 5, 22co 6073 . . . . 5 eval
2421, 23ccom 4874 . . . 4 eval
254, 7, 24csb 3243 . . 3 eval
262, 3, 25cmpt 4258 . 2 eval
271, 26wceq 1652 1 eval1 eval
 Colors of variables: wff set class This definition is referenced by:  evl1fval  19939
 Copyright terms: Public domain W3C validator