Description: The product of two nonnegative numbers is nonnegative. (Contributed by NM, 30-Jul-1999)
Ref | Expression | ||
---|---|---|---|
Hypotheses | lt2.1 | |- A e. RR |
|
lt2.2 | |- B e. RR |
||
Assertion | mulge0i | |- ( ( 0 <_ A /\ 0 <_ B ) -> 0 <_ ( A x. B ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lt2.1 | |- A e. RR |
|
2 | lt2.2 | |- B e. RR |
|
3 | mulge0 | |- ( ( ( A e. RR /\ 0 <_ A ) /\ ( B e. RR /\ 0 <_ B ) ) -> 0 <_ ( A x. B ) ) |
|
4 | 3 | an4s | |- ( ( ( A e. RR /\ B e. RR ) /\ ( 0 <_ A /\ 0 <_ B ) ) -> 0 <_ ( A x. B ) ) |
5 | 1 2 4 | mpanl12 | |- ( ( 0 <_ A /\ 0 <_ B ) -> 0 <_ ( A x. B ) ) |