Description: Absolute value and 'less than' relation. (Contributed by NM, 6-Apr-2005)
Ref | Expression | ||
---|---|---|---|
Hypotheses | sqrtthi.1 | |- A e. RR |
|
sqr11.1 | |- B e. RR |
||
Assertion | abslti | |- ( ( abs ` A ) < B <-> ( -u B < A /\ A < B ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sqrtthi.1 | |- A e. RR |
|
2 | sqr11.1 | |- B e. RR |
|
3 | abslt | |- ( ( A e. RR /\ B e. RR ) -> ( ( abs ` A ) < B <-> ( -u B < A /\ A < B ) ) ) |
|
4 | 1 2 3 | mp2an | |- ( ( abs ` A ) < B <-> ( -u B < A /\ A < B ) ) |