Theorem divge0i

Description: The ratio of nonnegative and positive numbers is nonnegative. (Contributed by NM, 12-Aug-1999)

	Ref	Expression
Hypotheses	ltplus1.1	|- A e. RR
	prodgt0.2	|- B e. RR
Assertion	divge0i	|- ( ( 0 <_ A /\ 0 < B ) -> 0 <_ ( A / B ) )

Proof

Step	Hyp	Ref	Expression
1		ltplus1.1	|- A e. RR
2		prodgt0.2	|- B e. RR
3		divge0	|- ( ( ( A e. RR /\ 0 <_ A ) /\ ( B e. RR /\ 0 < B ) ) -> 0 <_ ( A / B ) )
4	2 3	mpanr1	|- ( ( ( A e. RR /\ 0 <_ A ) /\ 0 < B ) -> 0 <_ ( A / B ) )
5	1 4	mpanl1	|- ( ( 0 <_ A /\ 0 < B ) -> 0 <_ ( A / B ) )