Syntax Definition wceq 1670

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 wffA=B here, and not in set theory where it belongs, is to allow us to express i.e. "prove" the weq 1671 of predicate calculus in terms of the wceq 1670 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 weq 1671 or wceq 1670, 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-cleq 2482 for more information on the set theory usage of wceq 1670.)

Hypotheses

Ref	Expression
wceq.cA	No typesetting for: class A
wceq.cB	No typesetting for: class B

Assertion

Ref	Expression
wceq	No typesetting for: wff A = B

See definition df-sb 1677 for more information.