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Syntax Definition wceq 1538
Description: Extend wff definition to include class equality.

For a general discussion of the theory of classes, see 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 1964 of predicate calculus in terms of the wceq 1538 of set theory, so that we do not "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 1964 or wceq 1538, 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 2794 for more information on the set theory usage of wceq 1538.)

Ref Expression
cA.wceq class 𝐴
cB.wceq class 𝐵
Ref Expression
wceq wff 𝐴 = 𝐵

See definition df-tru 1541 for more information.

Colors of variables: wff setvar class
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