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Syntax Definition wceq 1619
Description: Extend wff definition to include class equality.

For a general discussion of the theory of classes, see

(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 1620 of predicate calculus in terms of the wceq 1619 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 1620 or wceq 1619, 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 2249 for more information on the set theory usage of wceq 1619.)

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

This syntax is primitive. The first axiom using it is ax-8 1623.

Colors of variables: wff set class
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