Description: If the extended real negative is real, then the number itself is real. (Contributed by Glauco Siliprandi, 2-Jan-2022)
Ref | Expression | ||
---|---|---|---|
Hypotheses | xnegrecl2d.1 | |- ( ph -> A e. RR* ) |
|
xnegrecl2d.2 | |- ( ph -> -e A e. RR ) |
||
Assertion | xnegrecl2d | |- ( ph -> A e. RR ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xnegrecl2d.1 | |- ( ph -> A e. RR* ) |
|
2 | xnegrecl2d.2 | |- ( ph -> -e A e. RR ) |
|
3 | xnegrecl2 | |- ( ( A e. RR* /\ -e A e. RR ) -> A e. RR ) |
|
4 | 1 2 3 | syl2anc | |- ( ph -> A e. RR ) |