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Definition df-mon1 24116
Description: Define the set of monic univariate polynomials. (Contributed by Stefan O'Rear, 28-Mar-2015.)
Assertion
Ref Expression
df-mon1 Monic1p = (𝑟 ∈ V ↦ {𝑓 ∈ (Base‘(Poly1𝑟)) ∣ (𝑓 ≠ (0g‘(Poly1𝑟)) ∧ ((coe1𝑓)‘(( deg1𝑟)‘𝑓)) = (1r𝑟))})
Distinct variable group:   𝑓,𝑟

Detailed syntax breakdown of Definition df-mon1
StepHypRef Expression
1 cmn1 24111 . 2 class Monic1p
2 vr . . 3 setvar 𝑟
3 cvv 3348 . . 3 class V
4 vf . . . . . . 7 setvar 𝑓
54cv 1628 . . . . . 6 class 𝑓
62cv 1628 . . . . . . . 8 class 𝑟
7 cpl1 19768 . . . . . . . 8 class Poly1
86, 7cfv 6030 . . . . . . 7 class (Poly1𝑟)
9 c0g 16314 . . . . . . 7 class 0g
108, 9cfv 6030 . . . . . 6 class (0g‘(Poly1𝑟))
115, 10wne 2941 . . . . 5 wff 𝑓 ≠ (0g‘(Poly1𝑟))
12 cdg1 24040 . . . . . . . . 9 class deg1
136, 12cfv 6030 . . . . . . . 8 class ( deg1𝑟)
145, 13cfv 6030 . . . . . . 7 class (( deg1𝑟)‘𝑓)
15 cco1 19769 . . . . . . . 8 class coe1
165, 15cfv 6030 . . . . . . 7 class (coe1𝑓)
1714, 16cfv 6030 . . . . . 6 class ((coe1𝑓)‘(( deg1𝑟)‘𝑓))
18 cur 18715 . . . . . . 7 class 1r
196, 18cfv 6030 . . . . . 6 class (1r𝑟)
2017, 19wceq 1629 . . . . 5 wff ((coe1𝑓)‘(( deg1𝑟)‘𝑓)) = (1r𝑟)
2111, 20wa 383 . . . 4 wff (𝑓 ≠ (0g‘(Poly1𝑟)) ∧ ((coe1𝑓)‘(( deg1𝑟)‘𝑓)) = (1r𝑟))
22 cbs 16070 . . . . 5 class Base
238, 22cfv 6030 . . . 4 class (Base‘(Poly1𝑟))
2421, 4, 23crab 3063 . . 3 class {𝑓 ∈ (Base‘(Poly1𝑟)) ∣ (𝑓 ≠ (0g‘(Poly1𝑟)) ∧ ((coe1𝑓)‘(( deg1𝑟)‘𝑓)) = (1r𝑟))}
252, 3, 24cmpt 4860 . 2 class (𝑟 ∈ V ↦ {𝑓 ∈ (Base‘(Poly1𝑟)) ∣ (𝑓 ≠ (0g‘(Poly1𝑟)) ∧ ((coe1𝑓)‘(( deg1𝑟)‘𝑓)) = (1r𝑟))})
261, 25wceq 1629 1 wff Monic1p = (𝑟 ∈ V ↦ {𝑓 ∈ (Base‘(Poly1𝑟)) ∣ (𝑓 ≠ (0g‘(Poly1𝑟)) ∧ ((coe1𝑓)‘(( deg1𝑟)‘𝑓)) = (1r𝑟))})
Colors of variables: wff setvar class
This definition is referenced by:  mon1pval  24127
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