**Description: **Extend wff definition to
include the membership connective between
classes.
For a general discussion of the theory of classes, see
http://us.metamath.org/mpeuni/mmset.html#class.
(The purpose of introducing
here is to allow us to
express i.e. "prove" the wel 1871 of
predicate calculus in terms of the
wcel 1870 of set theory, so that we don't
"overload" the connective
with two syntax definitions. This is done to prevent ambiguity that
would complicate some Metamath parsers. The class variables and
are introduced
temporarily for the purpose of this definition but
otherwise not used in predicate calculus. See df-clab 2415 for more
information on the set theory usage of wcel 1870.) |