Theorem lttri2i

Description: Consequence of trichotomy. (Contributed by NM, 19-Jan-1997)

	Ref	Expression
Hypotheses	lt.1	|- A e. RR
	lt.2	|- B e. RR
Assertion	lttri2i	|- ( A =/= B <-> ( A < B \/ B < A ) )

Proof

Step	Hyp	Ref	Expression
1		lt.1	|- A e. RR
2		lt.2	|- B e. RR
3		lttri2	|- ( ( A e. RR /\ B e. RR ) -> ( A =/= B <-> ( A < B \/ B < A ) ) )
4	1 2 3	mp2an	|- ( A =/= B <-> ( A < B \/ B < A ) )