Theorem ltleni

Description: 'Less than' expressed in terms of 'less than or equal to'. (Contributed by NM, 27-Oct-1999)

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

Proof

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