This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem divgt0ii

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

Ref Expression
Hypotheses ltplus1.1 ⊢ 𝐴 ∈ ℝ
prodgt0.2 ⊢ 𝐵 ∈ ℝ
ltreci.3 ⊢ 0 < 𝐴
ltreci.4 ⊢ 0 < 𝐵
Assertion divgt0ii 0 < ( 𝐴 / 𝐵 )

Proof

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