Syntax Definition wceq 953

Description: Extend wff definition to include class equality.

(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 954 of predicate calculus in terms of the wceq 953 of set theory, so that we don't "overload" the = connective with two syntax definitions. This is done to prevent ambiguity that causes problems in 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 954 or wceq 953, 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 1461 for more information on the set theory usage of wceq 953.)

Hypotheses

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

Assertion

Ref	Expression
wceq	wff A = B

This syntax is primitive. The first axiom using it is ax-8 961.

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