Description: The center of a group is a normal subgroup. (Contributed by Stefan O'Rear, 6-Sep-2015)
Ref | Expression | ||
---|---|---|---|
Hypothesis | cntrnsg.z | |
|
Assertion | cntrnsg | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cntrnsg.z | |
|
2 | eqid | |
|
3 | eqid | |
|
4 | 2 3 | cntrval | |
5 | 1 4 | eqtr4i | |
6 | ssid | |
|
7 | 2 3 | cntzsubg | |
8 | 6 7 | mpan2 | |
9 | 5 8 | eqeltrid | |
10 | ssid | |
|
11 | 1 | cntrsubgnsg | |
12 | 9 10 11 | sylancl | |