Description: The polynomials over a field are a PID. (Contributed by Stefan O'Rear, 29-Mar-2015)
Ref | Expression | ||
---|---|---|---|
Hypothesis | ply1lpir.p | |
|
Assertion | ply1pid | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ply1lpir.p | |
|
2 | fldidom | |
|
3 | 1 | ply1idom | |
4 | 2 3 | syl | |
5 | isfld | |
|
6 | 5 | simplbi | |
7 | 1 | ply1lpir | |
8 | 6 7 | syl | |
9 | df-pid | |
|
10 | 9 | elin2 | |
11 | 4 8 10 | sylanbrc | |