Description: Elementhood in the centralizer. (Contributed by Mario Carneiro, 22-Sep-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | cntzfval.b | |
|
cntzfval.p | |
||
cntzfval.z | |
||
Assertion | elcntz | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cntzfval.b | |
|
2 | cntzfval.p | |
|
3 | cntzfval.z | |
|
4 | 1 2 3 | cntzval | |
5 | 4 | eleq2d | |
6 | oveq1 | |
|
7 | oveq2 | |
|
8 | 6 7 | eqeq12d | |
9 | 8 | ralbidv | |
10 | 9 | elrab | |
11 | 5 10 | bitrdi | |