Theorem ltnlei

Description: 'Less than' in terms of 'less than or equal to'. (Contributed by NM, 11-Jul-2005)

	Ref	Expression
Hypotheses	lt.1	|- A e. RR
	lt.2	|- B e. RR
Assertion	ltnlei	|- ( A < B <-> -. B <_ A )

Proof

Step	Hyp	Ref	Expression
1		lt.1	|- A e. RR
2		lt.2	|- B e. RR
3	2 1	lenlti	|- ( B <_ A <-> -. A < B )
4	3	con2bii	|- ( A < B <-> -. B <_ A )