Description: Recover the commutative law of addition for complex numbers from the Abelian group structure. (Contributed by NM, 17-Mar-2013) (Proof modification is discouraged.)
Ref | Expression | ||
---|---|---|---|
Assertion | cnaddcom | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid | |
|
2 | 1 | cnaddabl | |
3 | cnex | |
|
4 | 1 | grpbase | |
5 | 3 4 | ax-mp | |
6 | addex | |
|
7 | 1 | grpplusg | |
8 | 6 7 | ax-mp | |
9 | 5 8 | ablcom | |
10 | 2 9 | mp3an1 | |