Theorem ltnlei

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

	Ref	Expression
Hypotheses	lt.1	$$⊢A\in ℝ$$
	lt.2	$$⊢B\in ℝ$$
Assertion	ltnlei	$$⊢A<B\leftrightarrow \neg B\le A$$

Proof

Step	Hyp	Ref	Expression
1		lt.1	$$⊢A\in ℝ$$
2		lt.2	$$⊢B\in ℝ$$
3	2 1	lenlti	$$⊢B\le A\leftrightarrow \neg A<B$$
4	3	con2bii	$$⊢A<B\leftrightarrow \neg B\le A$$