Theorem divgt0ii

Description: The ratio of two positive numbers is positive. (Contributed by NM, 18-May-1999)

	Ref	Expression
Hypotheses	ltplus1.1	|- A e. RR
	prodgt0.2	|- B e. RR
	ltreci.3	|- 0 < A
	ltreci.4	|- 0 < B
Assertion	divgt0ii	|- 0 < ( A / B )

Proof

Step	Hyp	Ref	Expression
1		ltplus1.1	|- A e. RR
2		prodgt0.2	|- B e. RR
3		ltreci.3	|- 0 < A
4		ltreci.4	|- 0 < B
5	1 2 4	divgt0i2i	|- ( 0 < A -> 0 < ( A / B ) )
6	3 5	ax-mp	|- 0 < ( A / B )