Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > df-aa | Structured version Visualization version Unicode version |
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 ) of all polynomials in Poly, except the zero polynomial . (Contributed by Mario Carneiro, 22-Jul-2014.) |
Ref | Expression |
---|---|
df-aa | Poly |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caa 24069 | . 2 | |
2 | vf | . . 3 | |
3 | cz 11377 | . . . . 5 | |
4 | cply 23940 | . . . . 5 Poly | |
5 | 3, 4 | cfv 5888 | . . . 4 Poly |
6 | c0p 23436 | . . . . 5 | |
7 | 6 | csn 4177 | . . . 4 |
8 | 5, 7 | cdif 3571 | . . 3 Poly |
9 | 2 | cv 1482 | . . . . 5 |
10 | 9 | ccnv 5113 | . . . 4 |
11 | cc0 9936 | . . . . 5 | |
12 | 11 | csn 4177 | . . . 4 |
13 | 10, 12 | cima 5117 | . . 3 |
14 | 2, 8, 13 | ciun 4520 | . 2 Poly |
15 | 1, 14 | wceq 1483 | 1 Poly |
Colors of variables: wff setvar class |
This definition is referenced by: elaa 24071 |
Copyright terms: Public domain | W3C validator |