Description: If G is an inverse to F , then G is an isomorphism. (Contributed by Mario Carneiro, 3-Jan-2017)
Ref | Expression | ||
---|---|---|---|
Hypotheses | invfval.b | |
|
invfval.n | |
||
invfval.c | |
||
invfval.x | |
||
invfval.y | |
||
isoval.n | |
||
inviso1.1 | |
||
Assertion | inviso2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | invfval.b | |
|
2 | invfval.n | |
|
3 | invfval.c | |
|
4 | invfval.x | |
|
5 | invfval.y | |
|
6 | isoval.n | |
|
7 | inviso1.1 | |
|
8 | 1 2 3 4 5 | invsym | |
9 | 7 8 | mpbid | |
10 | 1 2 3 5 4 6 9 | inviso1 | |