Description: The negative of a real is real. (Contributed by Mario Carneiro, 28-May-2016)
Ref | Expression | ||
---|---|---|---|
Hypotheses | negidd.1 | |- ( ph -> A e. CC ) |
|
negrebd.2 | |- ( ph -> -u A e. RR ) |
||
Assertion | negrebd | |- ( ph -> A e. RR ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | negidd.1 | |- ( ph -> A e. CC ) |
|
2 | negrebd.2 | |- ( ph -> -u A e. RR ) |
|
3 | negreb | |- ( A e. CC -> ( -u A e. RR <-> A e. RR ) ) |
|
4 | 1 3 | syl | |- ( ph -> ( -u A e. RR <-> A e. RR ) ) |
5 | 2 4 | mpbid | |- ( ph -> A e. RR ) |