Theorem abslti

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 ) )

Proof

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 ) )