The Existence & Uniqueness command can only be used when you
have a goal of the form
!xP(x). If you select a goal of
this form and give the Existence & Uniqueness command, then Proof
Designer will say that to complete the proof you have to prove both
xP(x) and
x
y(P(x)
P(y)
x = y). The two parts of the proof are
labeled Existence and Uniqueness.