ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  wceq GIF version

Syntax Definition wceq 1332
Description: Extend wff definition to include class equality.

For a general discussion of the theory of classes, see https://us.metamath.org/mpeuni/mmset.html#class.

(The purpose of introducing wff 𝐴 = 𝐵 here, and not in set theory where it belongs, is to allow us to express i.e. "prove" the weq 1480 of predicate calculus in terms of the wceq 1332 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. For example, some parsers - although not the Metamath program - stumble on the fact that the = in 𝑥 = 𝑦 could be the = of either weq 1480 or wceq 1332, although mathematically it makes no difference. The class variables 𝐴 and 𝐵 are introduced temporarily for the purpose of this definition but otherwise not used in predicate calculus. See df-cleq 2133 for more information on the set theory usage of wceq 1332.)

Hypotheses
Ref Expression
cA.wceq class 𝐴
cB.wceq class 𝐵
Assertion
Ref Expression
wceq wff 𝐴 = 𝐵

See definition df-tru 1335 for more information.

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