Description: Centralizers in a monoid are preserved by monoid homomorphisms. (Contributed by Mario Carneiro, 24-Apr-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | cntzmhm.z | |
|
cntzmhm.y | |
||
Assertion | cntzmhm2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cntzmhm.z | |
|
2 | cntzmhm.y | |
|
3 | 1 2 | cntzmhm | |
4 | 3 | ralrimiva | |
5 | ssralv | |
|
6 | 4 5 | mpan9 | |
7 | eqid | |
|
8 | eqid | |
|
9 | 7 8 | mhmf | |
10 | 9 | adantr | |
11 | 10 | ffund | |
12 | simpr | |
|
13 | 7 1 | cntzssv | |
14 | 12 13 | sstrdi | |
15 | 10 | fdmd | |
16 | 14 15 | sseqtrrd | |
17 | funimass4 | |
|
18 | 11 16 17 | syl2anc | |
19 | 6 18 | mpbird | |