Description: If two structures have the same group components (properties), one is an Abelian group iff the other one is. (Contributed by NM, 6-Dec-2014)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ablpropd.1 | ||
ablpropd.2 | |||
ablpropd.3 | |||
Assertion | ablpropd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ablpropd.1 | ||
2 | ablpropd.2 | ||
3 | ablpropd.3 | ||
4 | 1 2 3 | grppropd | |
5 | 1 2 3 | cmnpropd | |
6 | 4 5 | anbi12d | |
7 | isabl | ||
8 | isabl | ||
9 | 6 7 8 | 3bitr4g |