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Syntax Definition wceq 1523
 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 1931 of predicate calculus in terms of the wceq 1523 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 1931 or wceq 1523, 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 2644 for more information on the set theory usage of wceq 1523.)
Hypotheses
Ref Expression
cA.wceq class 𝐴
cB.wceq class 𝐵
Assertion
Ref Expression
wceq wff 𝐴 = 𝐵