Definition

Let A and B be objects. Then we define A⊕B to be the object given by {x∈A∪B|¬x∈A∨¬x∈B}.

Background

The following background is necessary to understand this definition.

(.) Let A and x be objects. Then x∈A is a proposition.

(.) Let φ be a proposition. Then ¬φ is a proposition.

(.) Let φ and ψ be propositions. Then φ∨ψ is a proposition.

(.) Let A be an object. Let φ(a) be a proposition depending on a member a of A. Then {a∈A|φ(a)} is an object.

(.) Let A and B be objects. Then "A∪B" is an object.

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