For let D be made equal to A.
Since A, B are prime to one another, and A is equal to D, therefore D, B are also prime to one another.
Therefore each of the two numbers D, A is prime to B; therefore the product of D, A will also be prime to B. [VII. 24]
But the number which is the product of D, A is C.
Therefore C, B are prime to one another.
Q. E. D.