Description: The center is a subset of the base field. (Contributed by Thierry Arnoux, 21-Aug-2023)
Ref | Expression | ||
---|---|---|---|
Hypothesis | cntrss.1 | |- B = ( Base ` M ) |
|
Assertion | cntrss | |- ( Cntr ` M ) C_ B |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cntrss.1 | |- B = ( Base ` M ) |
|
2 | eqid | |- ( Cntz ` M ) = ( Cntz ` M ) |
|
3 | 1 2 | cntrval | |- ( ( Cntz ` M ) ` B ) = ( Cntr ` M ) |
4 | 1 2 | cntzssv | |- ( ( Cntz ` M ) ` B ) C_ B |
5 | 3 4 | eqsstrri | |- ( Cntr ` M ) C_ B |