Syntax Definition wcel 1105

Description: Extend wff definition to include the membership connective between classes.

(The purpose of introducing wff A e. B here is to allow us to express i.e. "prove" the wel 1106 of predicate calculus in terms of the wceq 1099 of set theory, so that we don't "overload" the e. connective with two syntax definitions. This is done to prevent ambiguity that causes problems in 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 1441 for more information on the set theory usage of wcel 1105.)

Hypotheses

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

Assertion

Ref	Expression
wcel	wff A e. B

This syntax is primitive. The first axiom using it is ax-13 1107.

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