Description: Closure of the group multiple (exponentiation) operation in a submonoid. (Contributed by Mario Carneiro, 13-Jan-2015)
Ref | Expression | ||
---|---|---|---|
Hypothesis | submmulgcl.t | |
|
Assertion | submmulgcl | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | submmulgcl.t | |
|
2 | eqid | |
|
3 | eqid | |
|
4 | submrcl | |
|
5 | 2 | submss | |
6 | 3 | submcl | |
7 | eqid | |
|
8 | 7 | subm0cl | |
9 | 2 1 3 4 5 6 7 8 | mulgnn0subcl | |