Description: 'Less than or equal to' relationship between subtraction and addition. (Contributed by NM, 30-Sep-1999) (Proof shortened by Andrew Salmon, 19-Nov-2011)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | lt2.1 | |- A e. RR |
|
| lt2.2 | |- B e. RR |
||
| lt2.3 | |- C e. RR |
||
| Assertion | lesubaddi | |- ( ( A - B ) <_ C <-> A <_ ( C + B ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | lt2.1 | |- A e. RR |
|
| 2 | lt2.2 | |- B e. RR |
|
| 3 | lt2.3 | |- C e. RR |
|
| 4 | lesubadd | |- ( ( A e. RR /\ B e. RR /\ C e. RR ) -> ( ( A - B ) <_ C <-> A <_ ( C + B ) ) ) |
|
| 5 | 1 2 3 4 | mp3an | |- ( ( A - B ) <_ C <-> A <_ ( C + B ) ) |