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Syntax Definition wcel 1409
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 1410 of predicate calculus in terms of the wceq 1259 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.)

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 1420.

Colors of variables: wff set class
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