Derive

Mathematically, to derive a statement something is to use logic, starting from known facts, or at the very beginning, from axioms, to decide whether the statement is true or false.

Formally, if you have a set of axioms A, then a set of statements B are all said to be derived if they follow logically from statements in A. And further, a set of statements C are said to be derived if they follow from statements in A and B.