Theorem lelttric

Description: Trichotomy law. (Contributed by NM, 4-Apr-2005)

	Ref	Expression
Assertion	lelttric	|- ( ( A e. RR /\ B e. RR ) -> ( A <_ B \/ B < A ) )

Proof

Step	Hyp	Ref	Expression
1		pm2.1	|- ( -. B < A \/ B < A )
2		lenlt	|- ( ( A e. RR /\ B e. RR ) -> ( A <_ B <-> -. B < A ) )
3	2	orbi1d	|- ( ( A e. RR /\ B e. RR ) -> ( ( A <_ B \/ B < A ) <-> ( -. B < A \/ B < A ) ) )
4	1 3	mpbiri	|- ( ( A e. RR /\ B e. RR ) -> ( A <_ B \/ B < A ) )