**Description: **Extend wff definition to
include the membership connective between
classes.
For a general discussion of the theory of classes, see
mmset.html#class.
(The purpose of introducing wff 𝐴 ∈ 𝐵 here is to allow us to
express, i.e., "prove", the wel 2157 of
predicate calculus in terms of the
wcel 2156 of set theory, so that we do not
"overload" the ∈ connective
with two syntax definitions. This is done to prevent ambiguity that
would complicate some Metamath parsers. The class variables 𝐴 and
𝐵 are introduced temporarily for the
purpose of this definition but
otherwise not used in predicate calculus. See df-clab 2793 for more
information on the set theory usage of wcel 2156.) |