Theorem ltnei

Description: 'Less than' implies not equal. (Contributed by NM, 28-Jul-1999)

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

Proof

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