Definition df-mzp 39665

Description: Polynomials over ℤ with an arbitrary index set, that is, the smallest ring of functions containing all constant functions and all projections. This is almost the most general reasonable definition; to reach full generality, we would need to be able to replace ZZ with an arbitrary (semi)ring (and a coordinate subring), but rings have not been defined yet. (Contributed by Stefan O'Rear, 4-Oct-2014.)

Assertion

Ref	Expression
df-mzp	⊢ mzPoly = (𝑣 ∈ V ↦ ∩ (mzPolyCld‘𝑣))

Detailed syntax breakdown of Definition df-mzp

Step	Hyp	Ref	Expression
1		cmzp 39663	. 2 class mzPoly
2		vv	. . 3 setvar 𝑣
3		cvv 3441	. . 3 class V
4	2	cv 1537	. . . . 5 class 𝑣
5		cmzpcl 39662	. . . . 5 class mzPolyCld
6	4, 5	cfv 6324	. . . 4 class (mzPolyCld‘𝑣)
7	6	cint 4838	. . 3 class ∩ (mzPolyCld‘𝑣)
8	2, 3, 7	cmpt 5110	. 2 class (𝑣 ∈ V ↦ ∩ (mzPolyCld‘𝑣))
9	1, 8	wceq 1538	1 wff mzPoly = (𝑣 ∈ V ↦ ∩ (mzPolyCld‘𝑣))

This definition is referenced by:  mzpval  39673  dmmzp  39674