Description: The order of an element is the same in a subgroup. (Contributed by Mario Carneiro, 14-Jan-2015) (Proof shortened by Stefan O'Rear, 12-Sep-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | submod.h | |
|
submod.o | |
||
submod.p | |
||
Assertion | subgod | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | submod.h | |
|
2 | submod.o | |
|
3 | submod.p | |
|
4 | subgsubm | |
|
5 | 1 2 3 | submod | |
6 | 4 5 | sylan | |