We prove that an associative commutative algebra U with derivations D 1 , . . . , D n ∈ Der U is an n-Lie algebra with respect to the n-multiplication D 1 ∧ · · · ∧ D n if the system {D 1 , . . . , D n } is in involution. In the case of pairwise commuting derivations this fact was established by V. T. Filippov. One more formulation of the Frobenius condition for complete integrability is obtained in terms of n-Lie multiplications. A differential system {D 1 , . . . , D n } of rank n on a manifold M m is in involution if and only if the space of smooth functions on M is an n-Lie algebra with respect to the Jacobian Det(D i u j ).