Theorem letrii

Description: Trichotomy law for 'less than or equal to'. (Contributed by NM, 2-Aug-1999)

	Ref	Expression
Hypotheses	lt.1	$$⊢A\in ℝ$$
	lt.2	$$⊢B\in ℝ$$
Assertion	letrii	$$⊢\left(A\le B\vee B\le A\right)$$

Proof

Step	Hyp	Ref	Expression
1		lt.1	$$⊢A\in ℝ$$
2		lt.2	$$⊢B\in ℝ$$
3	2 1	ltnlei	$$⊢B<A\leftrightarrow \neg A\le B$$
4	2 1	ltlei	$$⊢B<A\to B\le A$$
5	3 4	sylbir	$$⊢\neg A\le B\to B\le A$$
6	5	orri	$$⊢\left(A\le B\vee B\le A\right)$$