Description: Addition of 2 positive numbers is positive. (Contributed by NM, 16-May-1999) (Proof shortened by Andrew Salmon, 19-Nov-2011)
Ref | Expression | ||
---|---|---|---|
Hypotheses | lt2.1 | |- A e. RR |
|
lt2.2 | |- B e. RR |
||
Assertion | addgt0i | |- ( ( 0 < A /\ 0 < B ) -> 0 < ( A + B ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lt2.1 | |- A e. RR |
|
2 | lt2.2 | |- B e. RR |
|
3 | addgt0 | |- ( ( ( 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 ) ) |