Description: The addition operation of the field of complex numbers. (Contributed by Stefan O'Rear, 27-Nov-2014) (Revised by Mario Carneiro, 6-Oct-2015) (Revised by Thierry Arnoux, 17-Dec-2017) Revise df-cnfld . (Revised by GG, 27-Apr-2025)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | cnfldadd | |- + = ( +g ` CCfld ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | ax-addf | |- + : ( CC X. CC ) --> CC |
|
| 2 | ffn | |- ( + : ( CC X. CC ) --> CC -> + Fn ( CC X. CC ) ) |
|
| 3 | 1 2 | ax-mp | |- + Fn ( CC X. CC ) |
| 4 | fnov | |- ( + Fn ( CC X. CC ) <-> + = ( x e. CC , y e. CC |-> ( x + y ) ) ) |
|
| 5 | 3 4 | mpbi | |- + = ( x e. CC , y e. CC |-> ( x + y ) ) |
| 6 | mpocnfldadd | |- ( x e. CC , y e. CC |-> ( x + y ) ) = ( +g ` CCfld ) |
|
| 7 | 5 6 | eqtri | |- + = ( +g ` CCfld ) |