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Syntax Definition wcel 1710
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 wff A B here is to allow us to express i.e. "prove" the wel 1711 of predicate calculus in terms of the wceq 1642 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. 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 2340 for more information on the set theory usage of wcel 1710.)

Hypotheses
Ref Expression
wcel.cA class A
wcel.cB class B
Assertion
Ref Expression
wcel wff A B

This syntax is primitive. The first axiom using it is ax-13 1712.

Colors of variables: wff set class
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