Theorem subge0i

Description: Nonnegative subtraction. (Contributed by NM, 13-Aug-2000)

	Ref	Expression
Hypotheses	lt2.1	|- A e. RR
	lt2.2	|- B e. RR
Assertion	subge0i	|- ( 0 <_ ( A - B ) <-> B <_ A )

Proof

Step	Hyp	Ref	Expression
1		lt2.1	|- A e. RR
2		lt2.2	|- B e. RR
3		subge0	|- ( ( A e. RR /\ B e. RR ) -> ( 0 <_ ( A - B ) <-> B <_ A ) )
4	1 2 3	mp2an	|- ( 0 <_ ( A - B ) <-> B <_ A )