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Syntax Definition wcel 1873
Description: Extend wff definition to include the membership connective between classes.

For a general discussion of the theory of classes, see

(The purpose of introducing 
wff  A  e.  B here is to allow us to express i.e. "prove" the wel 1874 of predicate calculus in terms of the wcel 1873 of set theory, so that we don't "overload" the  e. connective with two syntax definitions. This is done to prevent ambiguity that would complicate some Metamath parsers. The class variables  A and  B are introduced temporarily for the purpose of this definition but otherwise not used in predicate calculus. See df-clab 2409 for more information on the set theory usage of wcel 1873.)

Ref Expression
wcel.cA  class  A
wcel.cB  class  B
Ref Expression
wcel  wff  A  e.  B

This syntax is primitive. The first axiom using it is ax-8 1875.

Colors of variables: wff setvar class
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