A helpful note from one of my logic graders
Victor writes:
"I noticed that nearly everyone has been making the same
mistake in problem 9 of 9-3. Save one person, everyone instantiated
with either x or y via UI and then later instantiated again using the
same free variable they instantiated with while using UI. This
violates the second restriction on EI, as (...w...) cannot have
appeared free anywhere else in the proof. Maybe you want to note that
to the class as nearly everyone made the same mistake. I learned that
you nearly always want to use EI before UI."
He's right. In general it's a good idea to instantiate existentials before
universals. (I may not have emphasized this enough in class.)