Think of mediant fractions

Algebra Level 1

$\dfrac{7}{13} < \dfrac{7 + 1}{13 + 1} < \dfrac{7 + 2}{13 + 2}$

The inequality above is true. Is the inequality below also true?

$\dfrac{7}{13} < \dfrac{7 + 1}{13 + 1} < \dfrac{7 + 2}{13 + 2} < \dfrac{7 + 3}{13 + 3}$