Theorem lttri3i

Description: Consequence of trichotomy. (Contributed by NM, 14-May-1999)

	Ref	Expression
Hypotheses	lt.1	|- A e. RR
	lt.2	|- B e. RR
Assertion	lttri3i	|- ( A = B <-> ( -. A < B /\ -. B < A ) )

Proof

Step	Hyp	Ref	Expression
1		lt.1	|- A e. RR
2		lt.2	|- B e. RR
3		lttri3	|- ( ( A e. RR /\ B e. RR ) -> ( A = B <-> ( -. A < B /\ -. B < A ) ) )
4	1 2 3	mp2an	|- ( A = B <-> ( -. A < B /\ -. B < A ) )