Suppose you have finite Sets $A$, $B$, $C$.
The function from $X \to_\text{total}Y$ represents a set of all of the total functions from set $X$ to set $Y$.
Ex:
Suppose $X$ is the set $\{1,0\}$, $Y$ is the set $\{3,4\}$
$X \to_\text{total}Y$ would be the set $\{(1,3)(0,3);(1,4)(0,4);(1,3)(0,4);(1,4)(0,3)\}$ which has four elements in it.
Now, the number of elements in $A\to_\text{total}(B\to_\text{total}$C)
will always equal the number of elements in $B\to_\text{total}(A\to_\text{total}$C).
(At least I think so, I tried with a few different sets by hand).
What is this property called?
It reminds me of the multiplicative property of equality but I don't think that's what it would be formally called, or if it is a property at all. I'm mainly looking for a better way to describe it than "I tried it on a bunch of different sets and it worked!"