Description: An extended real is real if and only if its extended negative is real. (Contributed by Glauco Siliprandi, 2-Jan-2022)
Ref | Expression | ||
---|---|---|---|
Hypothesis | xnegred.1 | |- ( ph -> A e. RR* ) |
|
Assertion | xnegred | |- ( ph -> ( A e. RR <-> -e A e. RR ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xnegred.1 | |- ( ph -> A e. RR* ) |
|
2 | xnegre | |- ( A e. RR* -> ( A e. RR <-> -e A e. RR ) ) |
|
3 | 1 2 | syl | |- ( ph -> ( A e. RR <-> -e A e. RR ) ) |