Description: The set of fixed points of F is the complement of the set of points moved by F . (Contributed by Thierry Arnoux, 17-Nov-2023)
Ref | Expression | ||
---|---|---|---|
Assertion | nfpconfp | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eldif | |
|
2 | fnelfp | |
|
3 | 2 | pm5.32da | |
4 | inss1 | |
|
5 | dmss | |
|
6 | 4 5 | ax-mp | |
7 | fndm | |
|
8 | 6 7 | sseqtrid | |
9 | 8 | sseld | |
10 | 9 | pm4.71rd | |
11 | fnelnfp | |
|
12 | 11 | notbid | |
13 | nne | |
|
14 | 12 13 | bitrdi | |
15 | 14 | pm5.32da | |
16 | 3 10 15 | 3bitr4rd | |
17 | 1 16 | syl5bb | |
18 | 17 | eqrdv | |