Description: 'Less than' relationship between subtraction and addition. (Contributed by NM, 17-Nov-2004)
Ref | Expression | ||
---|---|---|---|
Assertion | ltsub13 | |- ( ( A e. RR /\ B e. RR /\ C e. RR ) -> ( A < ( B - C ) <-> C < ( B - A ) ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ltaddsub | |- ( ( A e. RR /\ C e. RR /\ B e. RR ) -> ( ( A + C ) < B <-> A < ( B - C ) ) ) |
|
2 | ltaddsub2 | |- ( ( A e. RR /\ C e. RR /\ B e. RR ) -> ( ( A + C ) < B <-> C < ( B - A ) ) ) |
|
3 | 1 2 | bitr3d | |- ( ( A e. RR /\ C e. RR /\ B e. RR ) -> ( A < ( B - C ) <-> C < ( B - A ) ) ) |
4 | 3 | 3com23 | |- ( ( A e. RR /\ B e. RR /\ C e. RR ) -> ( A < ( B - C ) <-> C < ( B - A ) ) ) |