Theorem lttri4d

Description: Trichotomy law for 'less than'. (Contributed by NM, 20-Sep-2007) (Proof shortened by Andrew Salmon, 19-Nov-2011)

	Ref	Expression
Hypotheses	ltd.1	|- ( ph -> A e. RR )
	ltd.2	|- ( ph -> B e. RR )
Assertion	lttri4d	|- ( ph -> ( A < B \/ A = B \/ B < A ) )

Proof

Step	Hyp	Ref	Expression
1		ltd.1	|- ( ph -> A e. RR )
2		ltd.2	|- ( ph -> B e. RR )
3		lttri4	|- ( ( A e. RR /\ B e. RR ) -> ( A < B \/ A = B \/ B < A ) )
4	1 2 3	syl2anc	|- ( ph -> ( A < B \/ A = B \/ B < A ) )