Theorem

Let A and B be objects. Then we have B⊆A∪B.

Background

The following background is necessary to understand this theorem.

(.) Let A and B be objects. Then "A⊆B" is a proposition.

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

Background for Proof

The following background is necessary for the proof.

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

(.) Let A and B be objects. Assume for all x x∈A implies x∈B. Then we know A⊆B.

(.) Let A, B and x be objects. Assume x∈B. Then we know x∈A∪B.

Proof

We have for all x x∈B implies x∈A∪B. Using this, we conclude B⊆A∪B.

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