Theorem divgt0i

Description: The ratio of two positive numbers is positive. (Contributed by NM, 16-May-1999)

	Ref	Expression
Hypotheses	ltplus1.1	|- A e. RR
	prodgt0.2	|- B e. RR
Assertion	divgt0i	|- ( ( 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		divgt0	|- ( ( ( 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 ) )