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Syntax Definition wceq 1642
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 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 could be the of either weq 1643 or wceq 1642, 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 2346 for more information on the set theory usage of wceq 1642.)

Hypotheses
Ref Expression
wceq.cA
wceq.cB
Assertion
Ref Expression
wceq

See definition df-sb 1649 for more information.

Colors of variables: wff set class
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