Step 1: Understanding the Concept
Each electron in an atom is described by four quantum numbers \(n, l, m_l, m_s\).
Step 2: Statement
The rule that no two electrons in an atom can have the same set of all four quantum numbers is Pauli's exclusion principle.
Step 3: Compare the options
Hund's rule is about filling degenerate orbitals singly, the Aufbau rule is about filling order, and Heisenberg's principle is about uncertainty in position and momentum.
Final Answer:
The statement is Pauli's exclusion principle.
\[ \boxed{\text{(A) }\text{Pauli's exclusion principle.}} \]