Answer
In order to prove that there are exactly two elements $x$ and $y$ in a domain such
that P(x) and P(y) are true $Conjunction$ can be used.
Work Step by Step
Conjunction:
$\frac{p}{p \wedge q}$
A rule of inference that can be used is the conjunction because $P(x)$ and $P(y)$ are true and thus their conjunction is also true.
This rule of inference means that if you have two statements that are true, then their conjunction (first statement AND second statement) is also true.
