Is there a name for a biconditional that is itself conditional on something else?

Question

I'm trying to find whether there is a technical name for something like this:

$(A \iff B)$ given $C$

So $A$ and $B$ imply each other only if $C$ applies. For example, "August" and "hot" (fuzzily?) imply each other given that you are in the northern hemisphere.

Would it be reasonable to call this a second-order conditional? Since it is a conditional relationship that is itself conditional on something else.

Thanks!