Description: The product of two positive numbers is positive. (Contributed by NM, 18-May-1999)
Ref | Expression | ||
---|---|---|---|
Hypotheses | lt.1 | |- A e. RR |
|
lt.2 | |- B e. RR |
||
mulgt0i.3 | |- 0 < A |
||
mulgt0i.4 | |- 0 < B |
||
Assertion | mulgt0ii | |- 0 < ( A x. B ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lt.1 | |- A e. RR |
|
2 | lt.2 | |- B e. RR |
|
3 | mulgt0i.3 | |- 0 < A |
|
4 | mulgt0i.4 | |- 0 < B |
|
5 | 1 2 | mulgt0i | |- ( ( 0 < A /\ 0 < B ) -> 0 < ( A x. B ) ) |
6 | 3 4 5 | mp2an | |- 0 < ( A x. B ) |