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Definition df-plylt 42607
Description: Define the class of limited-degree polynomials. (Contributed by Stefan O'Rear, 8-Dec-2014.)
Assertion
Ref Expression
df-plylt Poly< = (𝑠 ∈ 𝒫 β„‚, π‘₯ ∈ β„•0 ↦ {𝑝 ∈ (Polyβ€˜π‘ ) ∣ (𝑝 = 0𝑝 ∨ (degβ€˜π‘) < π‘₯)})
Distinct variable group:   𝑠,𝑝,π‘₯

Detailed syntax breakdown of Definition df-plylt
StepHypRef Expression
1 cplylt 42605 . 2 class Poly<
2 vs . . 3 setvar 𝑠
3 vx . . 3 setvar π‘₯
4 cc 11146 . . . 4 class β„‚
54cpw 4606 . . 3 class 𝒫 β„‚
6 cn0 12512 . . 3 class β„•0
7 vp . . . . . . 7 setvar 𝑝
87cv 1532 . . . . . 6 class 𝑝
9 c0p 25626 . . . . . 6 class 0𝑝
108, 9wceq 1533 . . . . 5 wff 𝑝 = 0𝑝
11 cdgr 26149 . . . . . . 7 class deg
128, 11cfv 6553 . . . . . 6 class (degβ€˜π‘)
133cv 1532 . . . . . 6 class π‘₯
14 clt 11288 . . . . . 6 class <
1512, 13, 14wbr 5152 . . . . 5 wff (degβ€˜π‘) < π‘₯
1610, 15wo 845 . . . 4 wff (𝑝 = 0𝑝 ∨ (degβ€˜π‘) < π‘₯)
172cv 1532 . . . . 5 class 𝑠
18 cply 26146 . . . . 5 class Poly
1917, 18cfv 6553 . . . 4 class (Polyβ€˜π‘ )
2016, 7, 19crab 3430 . . 3 class {𝑝 ∈ (Polyβ€˜π‘ ) ∣ (𝑝 = 0𝑝 ∨ (degβ€˜π‘) < π‘₯)}
212, 3, 5, 6, 20cmpo 7428 . 2 class (𝑠 ∈ 𝒫 β„‚, π‘₯ ∈ β„•0 ↦ {𝑝 ∈ (Polyβ€˜π‘ ) ∣ (𝑝 = 0𝑝 ∨ (degβ€˜π‘) < π‘₯)})
221, 21wceq 1533 1 wff Poly< = (𝑠 ∈ 𝒫 β„‚, π‘₯ ∈ β„•0 ↦ {𝑝 ∈ (Polyβ€˜π‘ ) ∣ (𝑝 = 0𝑝 ∨ (degβ€˜π‘) < π‘₯)})
Colors of variables: wff setvar class
This definition is referenced by: (None)
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