Equating to each other?

Algebra Level 2

$\text{If }\ \dfrac AB = \dfrac CD\ \text{ and } \ A=C, \ \text{ then } \ B=D\, ?$

As shown above left, I have written up 2 fractions that are equal to each other.

If both the numerators are equal to each other, does this imply that both the denominators must be equal to each other as well?

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