Theorem lecasei

Description: Ordering elimination by cases. (Contributed by NM, 6-Jul-2007)

	Ref	Expression
Hypotheses	lecase.1	|- ( ph -> A e. RR )
	lecase.2	|- ( ph -> B e. RR )
	lecase.3	|- ( ( ph /\ A <_ B ) -> ps )
	lecase.4	|- ( ( ph /\ B <_ A ) -> ps )
Assertion	lecasei	|- ( ph -> ps )

Proof

Step	Hyp	Ref	Expression
1		lecase.1	|- ( ph -> A e. RR )
2		lecase.2	|- ( ph -> B e. RR )
3		lecase.3	|- ( ( ph /\ A <_ B ) -> ps )
4		lecase.4	|- ( ( ph /\ B <_ A ) -> ps )
5		letric	|- ( ( A e. RR /\ B e. RR ) -> ( A <_ B \/ B <_ A ) )
6	1 2 5	syl2anc	|- ( ph -> ( A <_ B \/ B <_ A ) )
7	3 4 6	mpjaodan	|- ( ph -> ps )