Theorem divgt0i2i

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

	Ref	Expression
Hypotheses	ltplus1.1	$$⊢A\in ℝ$$
	prodgt0.2	$$⊢B\in ℝ$$
	divgt0i2.3	$$⊢0<B$$
Assertion	divgt0i2i	$$⊢0<A\to 0<\frac{A}{B}$$

Proof

Step	Hyp	Ref	Expression
1		ltplus1.1	$$⊢A\in ℝ$$
2		prodgt0.2	$$⊢B\in ℝ$$
3		divgt0i2.3	$$⊢0<B$$
4	1 2	divgt0i	$$⊢\left(0<A\wedge 0<B\right)\to 0<\frac{A}{B}$$
5	3 4	mpan2	$$⊢0<A\to 0<\frac{A}{B}$$