Description: The inverse of a nonzero group element is a nonzero group element. (Contributed by Stefan O'Rear, 27-Feb-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | grpinvnzcl.b | |
|
grpinvnzcl.z | |
||
grpinvnzcl.n | |
||
Assertion | grpinvnzcl | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | grpinvnzcl.b | |
|
2 | grpinvnzcl.z | |
|
3 | grpinvnzcl.n | |
|
4 | eldifi | |
|
5 | 1 3 | grpinvcl | |
6 | 4 5 | sylan2 | |
7 | eldifsn | |
|
8 | 1 2 3 | grpinvnz | |
9 | 8 | 3expb | |
10 | 7 9 | sylan2b | |
11 | eldifsn | |
|
12 | 6 10 11 | sylanbrc | |