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Syntax Definition wceq 1395
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= here, and not in set theory where it belongs, is to allow us to express i.e. "prove" the weq 1733 of predicate calculus in terms of the wceq 1395 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 1733 or wceq 1395, 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 2449 for more information on the set theory usage of wceq 1395.)

Hypotheses
Ref Expression
cA.wceq No typesetting for: class A
cB.wceq No typesetting for: class B
Assertion
Ref Expression
wceq No typesetting for: wff A = B

See definition df-tru 1398 for more information.

Colors of variables: wff setvar class
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