Theorem divgt0i2i

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

	Ref	Expression
Hypotheses	ltplus1.1	⊢ 𝐴 ∈ ℝ
	prodgt0.2	⊢ 𝐵 ∈ ℝ
	divgt0i2.3	⊢ 0 < 𝐵
Assertion	divgt0i2i	⊢ ( 0 < 𝐴 → 0 < ( 𝐴 / 𝐵 ) )

Proof

Step	Hyp	Ref	Expression
1		ltplus1.1	⊢ 𝐴 ∈ ℝ
2		prodgt0.2	⊢ 𝐵 ∈ ℝ
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 ) )