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Syntax Definition wcel 1732
Description: Extend wff definition to include the membership connective between classes.

For a general discussion of the theory of classes, see http://us.metamath.org/mpeuni/mmset.html#class.

(The purpose of introducing wffAe.B here is to allow us to express i.e. "prove" the wel 1733 of predicate calculus in terms of the wcel 1732 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 and are introduced temporarily for the purpose of this definition but otherwise not used in predicate calculus. See df-clab 2476 for more information on the set theory usage of wcel 1732.)

Hypotheses
Ref Expression
wcel.cA No typesetting for: class A
wcel.cB No typesetting for: class B
Assertion
Ref Expression
wcel No typesetting for: wff A e. B

This syntax is primitive. The first axiom using it is ax-8 1734.

Colors of variables: wff set class
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