Description: Negative zero is a left additive identity. (Contributed by Steven Nguyen, 7-Jan-2023)
Ref | Expression | ||
---|---|---|---|
Assertion | reneg0addid2 | |- ( A e. RR -> ( ( 0 -R 0 ) + A ) = A ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elre0re | |- ( A e. RR -> 0 e. RR ) |
|
2 | rernegcl | |- ( 0 e. RR -> ( 0 -R 0 ) e. RR ) |
|
3 | elre0re | |- ( 0 e. RR -> 0 e. RR ) |
|
4 | renegid | |- ( 0 e. RR -> ( 0 + ( 0 -R 0 ) ) = 0 ) |
|
5 | 2 3 4 | readdid1addid2d | |- ( ( 0 e. RR /\ A e. RR ) -> ( ( 0 -R 0 ) + A ) = A ) |
6 | 1 5 | mpancom | |- ( A e. RR -> ( ( 0 -R 0 ) + A ) = A ) |