(The purpose of introducing wffA= here, and not in set theory
where it belongs, is to allow us to express i.e. "prove" the
weq1733
of
predicate calculus in terms of the wceq1395
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. For example, some parsers - although not the Metamath program
- stumble on the fact that the = in
could be the = of
either weq1733 or wceq1395, although mathematically it makes no
difference. The class variables and are introduced
temporarily for the purpose of this definition but otherwise not used in
predicate calculus. See df-cleq2449 for more information on the set
theory usage of wceq1395.)