Definition df-ply1 18334

Description: Define the algebra of univariate polynomials. (Contributed by Mario Carneiro, 9-Feb-2015.)

Assertion

Ref	Expression
df-ply1	|- Poly1 = ( r e. _V |-> ( (PwSer1 ` r ) ↾s ( Base ` ( 1o mPoly r ) ) ) )

Detailed syntax breakdown of Definition df-ply1

Step	Hyp	Ref	Expression
1		cpl1 18329	. 2 class Poly1
2		vr	. . 3 setvar r
3		cvv 3034	. . 3 class _V
4	2	cv 1398	. . . . 5 class r
5		cps1 18327	. . . . 5 class PwSer1
6	4, 5	cfv 5496	. . . 4 class (PwSer1 ` r )
7		c1o 7041	. . . . . 6 class 1o
8		cmpl 18115	. . . . . 6 class mPoly
9	7, 4, 8	co 6196	. . . . 5 class ( 1o mPoly r )
10		cbs 14634	. . . . 5 class Base
11	9, 10	cfv 5496	. . . 4 class ( Base ` ( 1o mPoly r ) )
12		cress 14635	. . . 4 class ↾s
13	6, 11, 12	co 6196	. . 3 class ( (PwSer1 ` r ) ↾s ( Base ` ( 1o mPoly r ) ) )
14	2, 3, 13	cmpt 4425	. 2 class ( r e. _V |-> ( (PwSer1 ` r ) ↾s ( Base ` ( 1o mPoly r ) ) ) )
15	1, 14	wceq 1399	1 wff Poly1 = ( r e. _V |-> ( (PwSer1 ` r ) ↾s ( Base ` ( 1o mPoly r ) ) ) )

This definition is referenced by:  ply1val  18346