Description: Any subset in a commutative monoid is a subset of its centralizer. (Contributed by AV, 12-Jan-2019)
Ref | Expression | ||
---|---|---|---|
Hypotheses | cntzcmnss.b | |
|
cntzcmnss.z | |
||
Assertion | cntzcmnss | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cntzcmnss.b | |
|
2 | cntzcmnss.z | |
|
3 | 1 2 | cntzcmn | |
4 | sseq2 | |
|
5 | 4 | eqcoms | |
6 | 5 | biimpd | |
7 | 6 | adantld | |
8 | 3 7 | mpcom | |