Equality of Algebraic Structures

Theorem
Two algebraic structures $$\left({S, \circ}\right)$$ and $$\left({T, *}\right)$$ are equal iff:


 * $$S = T$$
 * $$\forall a, b \in S: a \circ b = a * b$$

Proof
This follows from set equality and Equality of Ordered Pairs.