Description: Property of a monic polynomial. (Contributed by Stefan O'Rear, 5-Dec-2014)
Ref | Expression | ||
---|---|---|---|
Assertion | elmnc | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-mnc | |
|
2 | 1 | dmmptss | |
3 | elfvdm | |
|
4 | 2 3 | sselid | |
5 | 4 | elpwid | |
6 | plybss | |
|
7 | 6 | adantr | |
8 | cnex | |
|
9 | 8 | elpw2 | |
10 | fveq2 | |
|
11 | rabeq | |
|
12 | 10 11 | syl | |
13 | fvex | |
|
14 | 13 | rabex | |
15 | 12 1 14 | fvmpt | |
16 | 9 15 | sylbir | |
17 | 16 | eleq2d | |
18 | fveq2 | |
|
19 | fveq2 | |
|
20 | 18 19 | fveq12d | |
21 | 20 | eqeq1d | |
22 | 21 | elrab | |
23 | 17 22 | bitrdi | |
24 | 5 7 23 | pm5.21nii | |