Description: Real number version of addid1 , without ax-mulcom . (Contributed by SN, 23-Jan-2024)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | readdid1 | |- ( A e. RR -> ( A + 0 ) = A ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | resubid | |- ( A e. RR -> ( A -R A ) = 0 ) |
|
| 2 | id | |- ( A e. RR -> A e. RR ) |
|
| 3 | elre0re | |- ( A e. RR -> 0 e. RR ) |
|
| 4 | 2 2 3 | resubaddd | |- ( A e. RR -> ( ( A -R A ) = 0 <-> ( A + 0 ) = A ) ) |
| 5 | 1 4 | mpbid | |- ( A e. RR -> ( A + 0 ) = A ) |