|Description: This syntax construction
states that a variable , which has been
declared to be a set variable by $f statement vx, is also a class
expression. This can be justified informally as follows. We know that
the class builder is a class by cab 2282.
is distinct from
) we have by
cvjust 2291, we can argue that the syntax " " can be viewed as
an abbreviation for " ". See the
under the definition of class in [Jech] p. 4
showing that "Every set can
be considered to be a class."
While it is tempting and perhaps occasionally useful to view cv 1631 as a
"type conversion" from a set variable to a class variable, keep
that cv 1631 is intrinsically no different from any other
syntax such as cab 2282, cun 3163, or c0 3468.
For a general discussion of the theory of classes and the role of cv 1631,
(The description above applies to set theory, not predicate calculus. The
purpose of introducing
here, and not in set theory where it
belongs, is to allow us to express i.e. "prove" the weq 1633 of
calculus from the wceq 1632 of set theory, so that we don't
two syntax definitions. This is done to prevent
ambiguity that would complicate some Metamath