Definition df-mzp 40526

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 40524	. 2 class mzPoly
2		vv	. . 3 setvar 𝑣
3		cvv 3430	. . 3 class V
4	2	cv 1540	. . . . 5 class 𝑣
5		cmzpcl 40523	. . . . 5 class mzPolyCld
6	4, 5	cfv 6430	. . . 4 class (mzPolyCld‘𝑣)
7	6	cint 4884	. . 3 class ∩ (mzPolyCld‘𝑣)
8	2, 3, 7	cmpt 5161	. 2 class (𝑣 ∈ V ↦ ∩ (mzPolyCld‘𝑣))
9	1, 8	wceq 1541	1 wff mzPoly = (𝑣 ∈ V ↦ ∩ (mzPolyCld‘𝑣))

This definition is referenced by:  mzpval  40534  dmmzp  40535