Definition df-ply1 21705

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

Assertion

Ref	Expression
df-ply1	⊢ Poly1 = (𝑟 ∈ V ↦ ((PwSer1‘𝑟) ↾s (Base‘(1o mPoly 𝑟))))

Detailed syntax breakdown of Definition df-ply1

Step	Hyp	Ref	Expression
1		cpl1 21700	. 2 class Poly1
2		vr	. . 3 setvar 𝑟
3		cvv 3474	. . 3 class V
4	2	cv 1540	. . . . 5 class 𝑟
5		cps1 21698	. . . . 5 class PwSer1
6	4, 5	cfv 6543	. . . 4 class (PwSer1‘𝑟)
7		c1o 8458	. . . . . 6 class 1o
8		cmpl 21458	. . . . . 6 class mPoly
9	7, 4, 8	co 7408	. . . . 5 class (1o mPoly 𝑟)
10		cbs 17143	. . . . 5 class Base
11	9, 10	cfv 6543	. . . 4 class (Base‘(1o mPoly 𝑟))
12		cress 17172	. . . 4 class ↾s
13	6, 11, 12	co 7408	. . 3 class ((PwSer1‘𝑟) ↾s (Base‘(1o mPoly 𝑟)))
14	2, 3, 13	cmpt 5231	. 2 class (𝑟 ∈ V ↦ ((PwSer1‘𝑟) ↾s (Base‘(1o mPoly 𝑟))))
15	1, 14	wceq 1541	1 wff Poly1 = (𝑟 ∈ V ↦ ((PwSer1‘𝑟) ↾s (Base‘(1o mPoly 𝑟))))

This definition is referenced by:  ply1val  21717