Definition df-ply1 18787

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 18782	. 2 class Poly1
2		vr	. . 3 setvar r
3		cvv 3047	. . 3 class _V
4	2	cv 1445	. . . . 5 class r
5		cps1 18780	. . . . 5 class PwSer1
6	4, 5	cfv 5585	. . . 4 class (PwSer1 ` r )
7		c1o 7180	. . . . . 6 class 1o
8		cmpl 18589	. . . . . 6 class mPoly
9	7, 4, 8	co 6295	. . . . 5 class ( 1o mPoly r )
10		cbs 15133	. . . . 5 class Base
11	9, 10	cfv 5585	. . . 4 class ( Base ` ( 1o mPoly r ) )
12		cress 15134	. . . 4 class ↾s
13	6, 11, 12	co 6295	. . 3 class ( (PwSer1 ` r ) ↾s ( Base ` ( 1o mPoly r ) ) )
14	2, 3, 13	cmpt 4464	. 2 class ( r e. _V |-> ( (PwSer1 ` r ) ↾s ( Base ` ( 1o mPoly r ) ) ) )
15	1, 14	wceq 1446	1 wff Poly1 = ( r e. _V |-> ( (PwSer1 ` r ) ↾s ( Base ` ( 1o mPoly r ) ) ) )

This definition is referenced by:  ply1val  18799