For, since each of the numbers A, B is prime to C,
therefore the product of A, B will also be prime to C. [VII. 24]
But the product of A, B is E;
therefore E, C are prime to one another.
For the same reason E, D are also prime to one another.
Therefore each of the numbers C, D is prime to E.
Therefore the product of C, D will also be prime to E. [VII. 24]
But the product of C, D is F.
Therefore E, F are prime to one another.
Q. E. D.