Theorem ltleii

Description: 'Less than' implies 'less than or equal to' (inference). (Contributed by NM, 22-Aug-1999)

	Ref	Expression
Hypotheses	lt.1	$$⊢A\in ℝ$$
	lt.2	$$⊢B\in ℝ$$
	ltlei.1	$$⊢A<B$$
Assertion	ltleii	$$⊢A\le B$$

Proof

Step	Hyp	Ref	Expression
1		lt.1	$$⊢A\in ℝ$$
2		lt.2	$$⊢B\in ℝ$$
3		ltlei.1	$$⊢A<B$$
4	1 2	ltlei	$$⊢A<B\to A\le B$$
5	3 4	ax-mp	$$⊢A\le B$$