Proportional to 2 Separate Variables vs. Proportional to Product of 2 Variables
I guess some people may find this obvious, but I really don't. My question is:
If $A\propto B$ while $C$ is constant and $A\propto C$ while B remains constant, then why is $A\propto BC$ ?
Why $A$ has to be proportional to the product of $B$ and $C$ ?
Earlier I never really questioned this when it popped up in textbooks because for some reason I thought it was self-evident, but now I come to think of it, I really don't understand why this is true.
I guess people here could rigorously prove this which I would like to see but an intuitive explanation as to why this is true would also be really appreciated.