Theorem ltleii

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

	Ref	Expression
Hypotheses	lt.1	|- A e. RR
	lt.2	|- B e. RR
	ltlei.1	|- A < B
Assertion	ltleii	|- A <_ B

Proof

Step	Hyp	Ref	Expression
1		lt.1	|- A e. RR
2		lt.2	|- B e. RR
3		ltlei.1	|- A < B
4	1 2	ltlei	|- ( A < B -> A <_ B )
5	3 4	ax-mp	|- A <_ B