| Description: Extend wff definition to
include class equality.
For a general discussion of the theory of classes, see
https://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 1517
of
predicate calculus in terms of the wceq 1364
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 1517 or wceq 1364, 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 2189 for more information on the set theory usage
of
wceq 1364.) |
