**Description: **Extend wff definition to
include class equality.
For a general discussion of the theory of classes, see
http://us.metamath.org/mpeuni/mmset.html#class.
(The purpose of introducing wff
*A* = *B* here, and not in set theory
where it belongs, is to allow us to express i.e. "prove" the
weq 1643
of
predicate calculus in terms of the wceq 1642
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 *x* = *y*
could be the = of
either weq 1643 or wceq 1642, although mathematically it makes no
difference. The class variables *A* and *B* are introduced
temporarily for the purpose of this definition but otherwise not used in
predicate calculus. See df-cleq 2346 for more information on the set
theory usage of wceq 1642.) |