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Syntax Definition wcel 2156
Description: Extend wff definition to include the membership connective between classes.

For a general discussion of the theory of classes, see mmset.html#class.

(The purpose of introducing wff 𝐴𝐵 here is to allow us to express, i.e., "prove", the wel 2157 of predicate calculus in terms of the wcel 2156 of set theory, so that we do not "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 2793 for more information on the set theory usage of wcel 2156.)

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

This syntax is primitive. The first axiom using it is ax-8 2158.

Colors of variables: wff setvar class
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