I am trying to prove the statement in the form:
$\exists x \in S, \forall y \in \emptyset, P(x)$
where $P(x): x > y$ and $S$ is an arbitrary non-empty set.
My proof looks something like:
Let $x =$ some number in set S. Let $y \in \emptyset$. My intuition is that since we cannot check whether $x > y$ since $y$ is an empty set, the statement is vacuously true. My questions is, how do I write this "intuition" in a rigorous way?