MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  wcel Structured version   Visualization version   GIF version

Syntax Definition wcel 1987
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 1988 of predicate calculus in terms of the wcel 1987 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 2608 for more information on the set theory usage of wcel 1987.)

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 1989.

Colors of variables: wff setvar class
  Copyright terms: Public domain W3C validator