Set of 3 Integers each Divisor of Sum of Other Two

Theorem
There exists exactly one set of positive integers such that each is a divisor of the sum of the other two:
 * $\left\{ {1, 2, 3}\right\}$

Proof
We have that:
 * $5 \times 1 = 2 + 3$ so $1 \mathrel \backslash 2 + 3$
 * $2 \times 2 = 1 + 3$ so $2 \mathrel \backslash 1 + 3$
 * $1 \times 3 = 1 + 2$ so $3 \mathrel \backslash 1 + 2$