Description: Addition of 2 nonnegative numbers is nonnegative. (Contributed by NM, 28-May-1999) (Proof shortened by Andrew Salmon, 19-Nov-2011)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | lt2.1 | |- A e. RR |
|
| lt2.2 | |- B e. RR |
||
| Assertion | addge0i | |- ( ( 0 <_ A /\ 0 <_ B ) -> 0 <_ ( A + B ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | lt2.1 | |- A e. RR |
|
| 2 | lt2.2 | |- B e. RR |
|
| 3 | addge0 | |- ( ( ( A e. RR /\ B e. RR ) /\ ( 0 <_ A /\ 0 <_ B ) ) -> 0 <_ ( A + B ) ) |
|
| 4 | 1 2 3 | mpanl12 | |- ( ( 0 <_ A /\ 0 <_ B ) -> 0 <_ ( A + B ) ) |