Syntax Definition wsbc 1166

Description: Extend wff notation to include the proper substitution of a class for a set. Read this notation as "the proper substitution of class A for set variable x in wff φ."

(The purpose of introducing wff [A / x]φ here is to allow us to express i.e. "prove" the wsb 1167 of predicate calculus in terms of the wsbc 1166 of set theory, so that we don't "overload" its connectives with two syntax definitions. This is done to prevent ambiguity that causes problems in some Metamath parsers. The class variable A is introduced temporarily for the purpose of this definition but otherwise not used in predicate calculus. See df-sbc 1932 for more information on the set theory usage of wsbc 1166.)

Hypotheses

Ref	Expression
wph	wff φ
vx	set x
wsbc.cA	class A

Assertion

Ref	Expression
wsbc	wff [A / x]φ

See definition df-sb 1168 for more information.

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