Theorem divgt0i2i

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
	divgt0i2.3	|- 0 < B
Assertion	divgt0i2i	|- ( 0 < A -> 0 < ( A / B ) )

Proof

Step	Hyp	Ref	Expression
1		ltplus1.1	|- A e. RR
2		prodgt0.2	|- B e. RR
3		divgt0i2.3	|- 0 < B
4	1 2	divgt0i	|- ( ( 0 < A /\ 0 < B ) -> 0 < ( A / B ) )
5	3 4	mpan2	|- ( 0 < A -> 0 < ( A / B ) )