Definition df-aa 22880

Description: Define the set of algebraic numbers. An algebraic number is a root of a nonzero polynomial over the integers. Here we construct it as the union of all kernels (preimages of { 0 }) of all polynomials in (Poly ` ZZ ), except the zero polynomial 0p. (Contributed by Mario Carneiro, 22-Jul-2014.)

Assertion

Ref	Expression
df-aa	|- AA = U_ f e. ( (Poly ` ZZ ) \ { 0p } ) ( `' f " { 0 } )

Detailed syntax breakdown of Definition df-aa

Step	Hyp	Ref	Expression
1		caa 22879	. 2 class AA
2		vf	. . 3 setvar f
3		cz 10860	. . . . 5 class ZZ
4		cply 22750	. . . . 5 class Poly
5	3, 4	cfv 5570	. . . 4 class (Poly ` ZZ )
6		c0p 22245	. . . . 5 class 0p
7	6	csn 4016	. . . 4 class { 0p }
8	5, 7	cdif 3458	. . 3 class ( (Poly ` ZZ ) \ { 0p } )
9	2	cv 1397	. . . . 5 class f
10	9	ccnv 4987	. . . 4 class `' f
11		cc0 9481	. . . . 5 class 0
12	11	csn 4016	. . . 4 class { 0 }
13	10, 12	cima 4991	. . 3 class ( `' f " { 0 } )
14	2, 8, 13	ciun 4315	. 2 class U_ f e. ( (Poly ` ZZ ) \ { 0p } ) ( `' f " { 0 } )
15	1, 14	wceq 1398	1 wff AA = U_ f e. ( (Poly ` ZZ ) \ { 0p } ) ( `' f " { 0 } )

This definition is referenced by:  elaa  22881