Description: 'Less than or equal to' relationship between subtraction and addition. (Contributed by NM, 3-Aug-1999)
Ref | Expression | ||
---|---|---|---|
Hypotheses | lt2.1 | |- A e. RR |
|
lt2.2 | |- B e. RR |
||
lt2.3 | |- C e. RR |
||
Assertion | lesubadd2i | |- ( ( A - B ) <_ C <-> A <_ ( B + C ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lt2.1 | |- A e. RR |
|
2 | lt2.2 | |- B e. RR |
|
3 | lt2.3 | |- C e. RR |
|
4 | lesubadd2 | |- ( ( A e. RR /\ B e. RR /\ C e. RR ) -> ( ( A - B ) <_ C <-> A <_ ( B + C ) ) ) |
|
5 | 1 2 3 4 | mp3an | |- ( ( A - B ) <_ C <-> A <_ ( B + C ) ) |