Description: Addition to both sides of 'less than'. (Contributed by NM, 21-Jan-1997) (Proof shortened by OpenAI, 25-Mar-2020)
Ref | Expression | ||
---|---|---|---|
Hypotheses | lt.1 | |- A e. RR |
|
lt.2 | |- B e. RR |
||
lt.3 | |- C e. RR |
||
Assertion | ltadd2i | |- ( A < B <-> ( C + A ) < ( C + B ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lt.1 | |- A e. RR |
|
2 | lt.2 | |- B e. RR |
|
3 | lt.3 | |- C e. RR |
|
4 | ltadd2 | |- ( ( 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 ) ) |