Theorem leloei

Description: 'Less than or equal to' in terms of 'less than'. (Contributed by NM, 14-May-1999)

	Ref	Expression
Hypotheses	lt.1	|- A e. RR
	lt.2	|- B e. RR
Assertion	leloei	|- ( A <_ B <-> ( A < B \/ A = B ) )

Proof

Step	Hyp	Ref	Expression
1		lt.1	|- A e. RR
2		lt.2	|- B e. RR
3		leloe	|- ( ( A e. RR /\ B e. RR ) -> ( A <_ B <-> ( A < B \/ A = B ) ) )
4	1 2 3	mp2an	|- ( A <_ B <-> ( A < B \/ A = B ) )