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Syntax Definition wceq 1324
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 1325 of predicate calculus in terms of the wceq 1324 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 1325 or wceq 1324, 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.)

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 1328.

Colors of variables: wff set class
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