Principia mathematica, by Alfred North Whitehead ... and Bertrand Russell.

SECTION A.
UNIT CLASSES AND COUPLES.
Summary of Section A.
In this section we begin (*50) by introducing a notation for the relation
of identity, as opposed to the function "x = y"; that is, calling the relation
of identity I, we put
I= 9(x=y) Df.
The purpose of this definition is chiefly convenience of notation. The
definition enables us to speak of I, D'I, I R, aJ I, I"a, etc., which we
could not otherwise do.
At the same time we introduce diversity, which is defined as the negation
of identity, and denoted by the letter J. The properties of I and J result
imnmediately from *13, since
xly.. x= y.
We next introduce a very important notation, due to Peano, for the class
whose only member is x. If we took a strictly and purely extensional view
of classes, we should naturally suppose this class to be identical with x. But
in view of the theory of classes explained in *20, it is plain that x can never
be identical with a class of which it is a member, even when it is the only
member of that class. Peano uses the notation "tx" for the class whose
only member is x; we shall alter this to " 'x," following our general notation
for descriptive functions. Thus we are to have
L'x =Y (y = x) = Y (yIX) = I 'x.
Hence we take as our definition
t=I Df,
since this definition gives the desired value of tfx. The properties of l are
nmany and important.
It is important to observe that "t la" means "the only member of a."
Thus it exists when, and only when, a has one member and no more, in which
case a is of the form Lix, if x is its only member. Thus "tl a" means the
same as "(ix) (x e a)," and " t' (4Bz)" means the same as " (ix) (,x)." What
we call " t'a " is denoted, in Peano's notation, by " lo."