Description: Conditions for a function to be a univariate polynomial. (Contributed by Thierry Arnoux, 19-Aug-2023)
Ref | Expression | ||
---|---|---|---|
Hypotheses | fply1.1 | |
|
fply1.2 | |
||
fply1.3 | |
||
fply1.4 | |
||
fply1.5 | |
||
Assertion | fply1 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fply1.1 | |
|
2 | fply1.2 | |
|
3 | fply1.3 | |
|
4 | fply1.4 | |
|
5 | fply1.5 | |
|
6 | 2 | fvexi | |
7 | ovex | |
|
8 | 6 7 | elmap | |
9 | 4 8 | sylibr | |
10 | df1o2 | |
|
11 | snfi | |
|
12 | 10 11 | eqeltri | |
13 | 12 | a1i | |
14 | elmapi | |
|
15 | 13 14 | fisuppfi | |
16 | 15 | rabeqc | |
17 | 16 | oveq2i | |
18 | 9 17 | eleqtrrdi | |
19 | eqid | |
|
20 | eqid | |
|
21 | eqid | |
|
22 | 1oex | |
|
23 | 22 | a1i | |
24 | 19 2 20 21 23 | psrbas | |
25 | 18 24 | eleqtrrd | |
26 | eqid | |
|
27 | eqid | |
|
28 | eqid | |
|
29 | 27 28 3 | ply1bas | |
30 | 26 19 21 1 29 | mplelbas | |
31 | 25 5 30 | sylanbrc | |