Syntax Definition wceq 955

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 956 of predicate calculus in terms of the wceq 955 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 956 or wceq 955, 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 1468 for more information on the set theory usage of wceq 955.)

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-8 963.

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